Permutation Groups · Medium problem

Let $\pi = (1\,2\,3)(2\,4\,5) \in S_5$, where these two cycles share the point $2$ and so are NOT disjoint; compute the product by applying $(2\,4\,5)$ first, then $(1\,2\,3)$. Once $\pi$ is written as a product of disjoint cycles, how many fixed points does it have?