Conjugacy and the Class Equation · Easy problem

In $S_5$, let $\tau = (1\,2\,3)(4\,5)$ and $\rho = (2\,3\,5)(1\,4)$. Both have cycle type $(3,2)$, so they are conjugate. Matching the cycles in the order written (the $3$-cycle's entries to the $3$-cycle's entries, the $2$-cycle's entries to the $2$-cycle's entries) gives a permutation $\sigma$ with $\sigma\tau\sigma^{-1}=\rho$. What is $\sigma(2)$?