Answer
See below
Work Step by Step
The vertex is at $(-5, 2)$ and the focus is at $(-5, -1)$
The standard form for the parabola: $(x-h)^2=-4p(y-k)$
The distance from $(-5,2)$ to $(-5,-1)$ is $3$, so $p=3$
Plug in the given values: $(x+5)^2=-12(y-2)$