jmc

By the zero-product property, we have two cases: either $y=5$ or $x=-3$. If $x=-3$, $x^2=9$ and $y^2\ge 0$ so $x^2+y^2\ge 9$. If $y=5$, $y^2=25$ and $x^2\ge 0$, so $x^2+y^2\ge 25$. $x^2+y^2$ is clearly minimized in the first case with $x=-3$ and $y=0$ for a minimum of $\boxed{9}$.