Answer
focus $(0,-5)$, directrix $y=5$
see graph.
Work Step by Step
Step 1. Given $x^2=-20y$, we have $4p=-20$ and $p=-5$ with the parabola opening downwards and vertex at $(0,0)$.
Step 2. We can find the focus at $(0,-5)$ and directrix as $y=5$
Step 3. We can graph the parabola as shown in the figure.