Isomorphism and Subgraphs · Hard problem

Let $P_5$ be the path $1\text{-}2\text{-}3\text{-}4\text{-}5$ (edges $12,23,34,45$). What is the minimum number of edges you must add to $P_5$ (keeping its $4$ edges and adding to them, possibly after relabeling the vertices) to reach a graph isomorphic to $K_{2,3}$?