Graph Coloring · Challenge problem

Let $G$ be formed by taking the $5$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}1$ together with two new vertices $6,7$ joined to EACH OTHER and to every one of $1,\ldots,5$ ($5+1+10=16$ edges in all). What is $\chi(G)$?