I'm planning on adding a lot of content and somewhat revamping this guide sometime over the next couple weeks so it'll (hopefully) be easier to understand, I'll make it a priority so keep your eyes peeled.

Introduction
Hi, I'm the dude with an obnoxious amount of 0s in his name in stream chats... Guess who that is xD
Anyway, I'm writing a guide for all the baby terrans out there about my favorite TvZ build - the +1 5Rax, and I'm sure all of you know what that is. This guide will be an a somewhat in-depth look of this build, how to use it, and its transitions.
The +1 5Rax is a strong build particularly against the very common 3Hatch muta. The reason being is that the +1 5Rax hits a timing where the zerg does not yet have lurkers to protect his third base, meaning he has to fight a constant stream of +1 MnM with purely muta/ling for an amount of time until his lurkers are out. One of the best parts of this build however, is that it is not imperative to kill the zerg's third base. If you manage to be cost efficient and force the zerg to spend his larva on zerglings instead of drones, then you have done enough damage for the time being since the build naturally secures map control long enough for you to get your tech buildings up.
The Build Order
So, I do not like writing a list of build orders on specific supplies because you might lose an extra scv than how I picture in my mind, so I am going to write the order you want to make buildings. Just make buildings when you have the money.
The following will be a 1Rax FE opener(Make scvs constantly until I say)
Supply depot
Barracks(Make marines once it finishes)
supply Depot
Command Center (See notes)
Refinery
Engineering Bay (See notes)
+1 Infantry weapon as soon as ebay finishes
Academy
Stop SCV production around high 30s of supply so you can get your barracks down, resume from there)
Barracks x4 (So you'll have 5)

Some notes: 1rax fe is flexible in that if you scout a 12 hatch on the first position you scout, you can skip your first marine and build a command center at 15, a supply depot, and then start marine productions there.
When you +1 5 rax, pull scvs off gas as soon as you hit 100 gas, and put them back on when your academy starts.
Also, you should build a bunker just for safe measure somewhere between your engineering bay a start of your barracks, maybe even sooner if your scout did not live long enough to determine a ling all in etc.
Build comsats as soon as you can. While your comsats is also a great time to make your barracks, because you should be in the 30 supplies so you actually won't be cutting many scvs. I personally usually make my barracks as my comsats are building. *You can choose to slightly delay your comsats and make a couple barracks before the comsats so you get out a couple more scvs(with the 50 minerals at each cc rather than the 50 for comsats), but don't make the comsats too late. You don't want to be unprepared for either/or 3hatch muta and 3hatch lurker. Comsat timing is relative to your own game sense and knowing when the zerg's spire should pop. This means if your timing estimate is correct then you can build your comsats whenever you want in order to see his tech path.
+1 5Rax is most effective against 3 hatch muta, less strong against 3 hatch lurker, and not to be used against 2 hatch builds. 2 hatch builds come too early and your upgrades are not done yet. I would recommend using a +1 4rax instead. What to do against 3 hatch lurker will be explained farther down.
Some people like to put down the 4 more rax at the same time. It doesn't matter that much really. I personally just put them down each when I have the money.
Now the fun part: What to do now that you have 5 barracks, +1 upgrade, and a ball of MnM.
The most ideal time to move out is when you have 16 - 20 marines and 4-5 medics. If timed correctly, his mutas should be about to pop. This is when you move out. One key to +1 5rax is that you can skimp on turrets because you are making his mutas defend his third base.
Notes: You can move out sooner with 12 marines + 3 medics and add on reinforcements to there, but it is dangerous if you are in the dark. Only do this if you counted his drones, took account any creep colonies, and you know he did not make many zerglings. At that point, you can move out with 12 marines rather than the 16+ and reinforce the group from there.
+1 armor is to be upgraded immediately after +1 weapons. While you move out, you should start your factory as well. What to do with your tech will be discussed farther down.
The primary reason for this build is that you are making the zerg go to your marines and medics instead of keeping you in your base, which is what 3 hatch muta aims to do. Before lurkers have popped, your group of units is more than capable of taking out the zerg's third base, and should be a priority. If his lurkers came out in time and you were unable to kill his third base, you have nothing to fear, just move around the map with an increasing ball of MnM and pose a threat with them and avoid getting contained. At this point, your factory should at least be up.
Remember: Pose a threat with your units, and, especially early on; Be aggressive. Pick off any stray lurkers you see, burrowed or unburrowed. You can reinforce quickly off of a quick 5 barracks, and he is locked into making units.
At this point, the phase of +1 5Rax is over; his hive has started, and it's time to transition.
Also, when transitioning into the midgame, build two bunkers or so at the front of your natural just to be safe from lurker/ling backstabs. It's just a precaution, you can choose not to if you have terrific scouting and are prepared in advance for it in some other way.
DO NOT ALLOW HIM TO TAKE ANOTHER THIRD IF YOU TAKE HIS PLANNED ONE DOWN. YOU ARE IN A FANTASTIC POSITION IF YOU KILL HIS THIRD BASE AND YOU CAN TRANSITION INTO MNM + TANK + VESSEL IN THIS SITUATION BECAUSE HE WILL NOT HAVE THE GAS ON 2 BASES TO SUPPORT LURKERS AND DEFILERS, SO CONSTANTLY PELT HIM UNTIL HE DIES. I HAVE LOST GAMES BECAUSE OF POOR SCOUTING FOR ANOTHER THIRD - DON'T LET THIS HAPPEN.
IMPORTANT: Against any competent zerg, if you didn't take out his third, the lovable tank + vessel pre-hive push is significantly later than what you will be used to so it will unlikely work. It is almost not worth using it; it will not be in time because his defilers will about to finish consume by the time you're at his front door, but if you want to make a few tanks and attempt it, you can. It's not recommended by me though. Don't expect it to win the game. This is one thing that separates +1 5rax and +1 4rax; Your tech is later in exchange for much more beneficial lurker snipes since you can reinforce faster and keep your map control.
Transitions
SK Terran + 3rd base + 2/3fac mines
This is probably the build most people will be used to. While your marines were pressuring him, you should have been adding tech buildings. By tech buildings, I mean two factories and two starports. Don't forget upgrades as well. And yes, two factories. Stream vultures with speed + mines out of them, use them to secure a third base, and pose a threat/gain map control. Add barracks as necessary and pump vessels from 2 starports. Play this style as a standard SK terran + mines - Establish map control, and take a 4th/whatever and slowly transition into mech if you can't end the game here. Note: As the game is progressing, you should start making a few tanks to position outside/inside your bases just incase the zerg makes it to your side of the map. Stay aggressive though. The biggest goal of lategame TvZ is keeping the pressure on him so he can't go to you. It's up to you to determine when the mech switch is; I can't tell you. There are too many variables.
SK Terran + 3rd base + 1fac mines
This is the same but with a couple extra barracks rather than another factory and less mines. I don't recommend this because it's definitely worth it to have the extra mines.
Hardcore SK Terran
I am listing this for the sake of listing transitions. By hardcore SK Terran, I mean you are trying to be Nada and win the game with Marines, Medics, and Science Vessels. Not recommended.
+1 5Rax --> 3Fac + 5rax --> Mech Transition
This is my favorite build, and I sincerely believe that it is the overall strongest. What you do here is, while you're pressuring the zerg during his lair tech, you add three factories and two armories after they finish, and upgrade from them. You will be pumping vultures out of three factories, which is more than enough at this stage of the game to secure a third. When the third is up, start making tanks, lift all 5 of your rax and put them at key points. You will have leftover bio to be pressuring with and you can bring your tank/vulture/goliaths/scvs(for turrets) up to establish a mech line infront of the zerg's bases while you take your half of the map. One of the primary strengths of this build is that the zerg shouldn't really know what's up until he notices the absurd amount of vultures. At an early point in the game before most zergs sunken their third, you can runby with vultures. Be extremely annoying with the vultures you are making from 3 factories. It's hard to describe what exactly you should be doing after the full on mech switch has happened; all I can say is pressure him. There are just too many variables that could have occured up to late game scenarios that I can't tell you; you have to play on feel at this point.
Notes: You do not go beyond 1/1 infantry with this build, and you can choose whether or not to get vessels(Getting vessels means you will have less tanks). Add your starport and science facility when the mech upgrades are approaching halfway done if you do not get vessels. You can choose to lift your starport out to act as one of your barracks or make dropships with it for vulture harass. Your ultimate goal is to make the zerg leave from pressure or to get into an unkillable spot in a split map situation.
DISCLAIMER: I have just recently started using this. I used to use the SK Terran + mines, but this build suits my style a lot more I feel. I might even be doing it wrong, I'm just sharing my view and how I think of it.
2fac Tanks, 1port vessel, infantry
I don't know what to call this, but you are making units and constantly pressuring with infantry off of however many bases you have, 2 factories of tanks, and a single starport of vessels. This is another one I'm listing for the sake of transitions. I don't know what to tell you about this, I don't use it.
Game Flow
This build is significantly different from the rax + tech builds because you are constantly moving around the map with a growing army, rather than staying in your base and emerging with a strong pre-hive attack. You must have an aggressive mind set but just don't be too reckless. Remember that the tank + vessel timing used by the rax + tech builds does not work with +1 5rax because it is quite delayed. Instead, you are setting up for more lategame oriented play if you can't kill him with usage of mines and/or tanks and map splitting, as opposed to trying to kill the zerg before his defilers and consume are ready.
Reaction to: 3 hatch lurker --> hive
Against 3 hatch lurker, you have to play in a stage as if you were unable to kill his third base, his mutas are dead, and he has fielded a lurker/ling or hydra/lurk army. Your primary goal is to not get contained until your tech is out; it's that simple. Play it out with any transition you want and head to the lategame without falling behind. Be a bit more cautious about fighting his lurkers but definitely do so if the situation favors you; just be careful, because getting contained is a very big danger.
Reaction to: Hydra Lurk
Do what you want but have two factories making tanks with it. I have not encountered this build itself many times, and I have not encountered it using +1 5rax. However, tanks are good against both of these units. Make tanks.
Reaction to: 2 hatch muta
Don't use +1 5rax. I recommend +1 4rax or a #rax tech build.
Reaction to: Whatever
Use your brain, I don't have time/the will to list every single possible thing the zerg can do.
+1 5Rax vs +1 4Rax
The +1 5Rax has a stronger and faster reinforcing bio army during the point where zerg does not have lurkers and while the zerg gets his hive. However, the +1 5rax tank + vessel push is delayed so much that it will very rarely win the game, whereas with +1 4rax it is still worth doing it to pose a huge threat. Some people think +1 5rax is more forgiving on bad micro because you can reinforce faster; they're wrong. The reason is that the game flow is so reliant on your early bio that you cannot afford to carelessly lose your MnM. Of course I'm not saying you cannot afford it with +1 4rax either, but you get the jist of it. I'm saying that if anything, it is less forgiving on poor micro.
Maps to use this build on
Good:
La Mancha (DEFINITELY)
Fighting Spirit
Circuit Breaker
Splittable Maps that don't have anti-terran features
Maps where you can zergling tight the natural because this build does have a danger zone against ling allins.
Bad:
Everything else..? --
Conclusion
I don't know whether or not this guide will be useful or rust away into the archives of tl, but I did have a bit of fun writing it, so I hope you guys enjoy reading it. I know many terrans use 2 or 3rax tech so this build is a good way to vary your style and become more flexible in general.
I realize that I mention map splitting a lot in this guide and I do realize that Pro7ect is one the only ones that can actually map split smoothly and beautifully, but a lot of us aren't facing super strong players so just do the best you can with it. I will probably add some content to this guide because I am bound to have forgotten some details, and feel free to post if you disagree with the way I use/look at this build.
Also, regarding some replays of myself, I don't have any unless you guys want to see lumire get pummeled constantly unless he cheeses. Well, at the time of posting, I do have one, so if anyone actually made it to reading this part, I would greatly appreciate if someone told me how to upload replays and I'll do it ASAP.
Replays
COMING SOON
Progamer Reference
I'm too lazy to go searching because it's 12:14A.M right now, but off the top of my head, this is a great game: (I will add more to this part as well later on)
http://www.teamliquid.net/tlpd/korean/games/71328_Flash_vs_ZerO/vod
I'm gonna count how many times I edit this. Right now: 6