smc

Assume one of the segments bisected by the inscribed square has length $x$. Thus, the alternate segment has length $7-x$. Applying Pythagorean's Theorem, $x^2+(x-7{)}^2=5^2$. Simplifying, $(x-3)(x-4)=0$, so $x=3$ or $x=4$ (it does not matter, as rotations produce the same figure). The longest line that can be made forms a right triangle with legs of $4$ and $7$. $\sqrt{4^2+7^2}=\sqrt{65}\to \boxed{\sqrt{65}}$