OMCC 2011 Problem 3

A slip on an integer $n\geq 2$ is an operation that consists in choosing a prime divisor $p$ of $n$ and replacing $n$ by $\frac{n+p^2}{p}.$

Starting with an arbitrary integer $n\geq 5$ , we successively apply the slip operation on it. Show that one eventually reaches $5$ , no matter the slips applied.