Answer
$(-5, 0)$
Work Step by Step
The vertex-form of a quadratic function is $y=a(x-h)^{2}+k$ where the vertex is the opposite of $h$ and $k$, or $(h, k)$. Given the function from the problem, $g(x)=(x+5)^{2}$, written in vertex form this function looks like $f(x)=1(x-(-5))^{2}+0$. Therefore the vertex is at $(-5, 0)$.