S5 Permutations: Can a & b Create Cycle d?

[bokasabi]

Homework Statement

can cycles a and b create cycle d?
let cycle a = 123
cycle b=12345
cycle d = 12

i.e. can some combination of a and b = d

Homework Equations

only working in S5

The Attempt at a Solution

I have tried various different permutations, 23 over all, things like aba, ab(a^-1), bab, (b^2)a(b^2)
things like this. I am not sure if a solution exists but I have been trying differnt guesses for hours. I don't want to try 120 times to get it.

 

[AKG]

Do you know what odd and even permutations are?

 

[HallsofIvy]

Good hint!