Just a little confused about conjugacy class equations.

Example:

In the symmetric group $\displaystyle S_5$ how many elements are there in the conjugacy class of the element $\displaystyle (12)(34)$?

I get that this is the amount of different possible ways to have a possible combination of 2 2 1 in $\displaystyle S_5$, and I know the answer's 15, I'm just not sure how to calculate this.

Thanks in advance