The Sylow Theorems · Hard problem

A group of order $1125=3^2\cdot5^3$ has normal Sylow subgroups $P\cong\mathbb Z_9$ and $Q\cong\mathbb Z_{125}$ (cyclic) that intersect trivially and together generate $G$, so $G\cong \mathbb Z_9\times\mathbb Z_{125}$. How many elements of $G$ have order exactly $15$?