Write the standard form of a parabola with focus at (0,-5) and directrix y=5

This is a vertical parab because the directrix is horiz. It opens down, because the directrix is above the focus. The vertex is (0,0), half way between the focus and the directrix. Thus, p = - 5. Let's use this info

4py = x^2

Here, 4 (-5) y = x^2, or - 20y = x^2, or y = (-1/20) x^2