small brain teaser... enjoy

1-4 are false, 5 is true.

assuming they start as true, it's 1,2 and 4 false, 3 and 5 true.
assuming they start as false, it's the opposite

Assuming 1-5 are all 1t-5t, 1-4 will be false and 5 is true.

I think no solution
To put it this way, let's consider 1's statement: "2,3 are false"

Assume 1t, then 2f 3f.
Assume 1f, then 2t 3t.

As we can see, no matter 1's true/falseness, 1 and 3 will always be opposite. Either 1t 3f, or 1f 3t.

Now let's consider 5's statement: "1, 3 are true"

Assume 5t, then 1t 3t
Assume 5f, then 1f 3f

As we can see, no matter 5's true/falseness, 1 and 3 will always be the same, Either 1t 3t, or 1f 3f.

Thus we reach a contradiction >_< Thus no solution I guess.

if 1 is true, then 2 and 3 are false (as stated) => 1 is true and 3 is false (so far so good) and 4 is true, 5 is false (the reverse of 3) => 2 is true, 3 is false and 1 is false and 3 is true - contradiction with the initial presupposition

if 1 is false, then 2 and 3 are true => 1 is false, 3 is true and 4 is false, 5 is true => 2 is false, 3 is true (the reverse of 4) and 1 is true - contradicting the initial supposition

So 1 can't be true or false, therefore the exercise has no solution?

1: true
2: false
3: false
4: false
5: false

When you set, f.e., (1) to FALSE you get 3 optional REAL statusses:
-(2) FALSE, (3) TRUE
-(2) TRUE, (3) FALSE
-(2) TRUE, (3) TRUE

Maybe I'm doing it wrong, but it looks like the only one that never changes is statement 5 (by the time you read statement 3 it always says statement 5 is true, and it's the only statement that can change 5), but 5 can't be true because 1 says statement 2&3 are true/false (depending on whether it's been reversed) and statement 2 never agrees that both statement 1 and statement 3 are true.... just looking at it, I'd say that statements 2 or 3 can be true, but not both of them... and I'm not sure how to determine which if either of them are true. Statements 1, 4 and 5 look to be definitely false.

statement 1) 2 and 3 are false.

1=
2=f
3=f
4=
5=

statement 2) 1 is false, 3 is true.

1=f
2=f
3=ft
4=
5=

statement 3) 4 is false, 5 is true.

1=
2=f
3=f
4=ftf
5=t

statement 4) 2 is true, 3 is false.

1=
2=ft
3=ff
4=ftf
5=t

statement 5) 1 is true, 3 is true.

1=t
2=ft
3=fft
4=ftf
5=t

2 false cancel out, no matter how many true's, a leftover false will make the statment false.
end result:

1=t
2=f
3=t
4=t
5=t

statement 1) 2 and 3 are false.
statement 2) 1 is false, 3 is true.
statement 3) 4 is false, 5 is true.
statement 4) 2 is true, 3 is false.
statement 5) 1 is true, 3 is true.

1) says 2 and 3 are false.
2) can no longer say 1 is false and 3 is true. it now says 1 is true and 3 is false
3) can no longer say 4 is false and 5 is true. it now says 4 is true and 5 is false.
4) says 2 is true, and 3 is false.
5) can no longer say 1 is true, 3 is true. now says 1 is false, 3 is true.

remember: one statement saying another statement is true, therefore keeps the statement the same.

the curren't status of the statements are:

1=tf
2=ft
3=ffft
4=t
5=f

final answer:

1=f
2=f
3=f
4=t
5=f

statement 1) 2 and 3 are false.
statement 2) 1 is false, 3 is true.
statement 3) 4 is false, 5 is true.
statement 4) 2 is true, 3 is false.
statement 5) 1 is true, 3 is true.
Starting at 1 = T

T 1) 2 false, 3 false
F 2) 1 true, 3 false
F 3) 4 true, 5 false
T 4) 2 false, 3 true

go back to 3)

T 3) 4 false, 5 true
F 4) 2 true, 3 false

go back to 2)

T 2) 1 false, 3 true

go back to 1)

F 1) 2 true 3 true
T 2) 1 false, 3 true
T 3) 4 false, 5 true
F 4) 2 true, 3 false

Loop???