Walks, Paths and Connectivity · Medium problem

A graph on vertices $1,2,3,4,5$ consists of a square $1\text{-}2\text{-}3\text{-}4\text{-}1$ with an extra vertex $5$ joined to both $1$ and $2$ (edges $12,23,34,41,15,25$). How many distinct paths (no repeated vertex) of length exactly $3$ run from vertex $4$ to vertex $5$?