Final answer:
The equation for the parabola is x² = 4a(y + 5).
Step-by-step explanation:
The equation for a parabola with a focus at (0,-5) and a directrix at y=-3 can be written in the vertex form as:
(x - h)² = 4a(y - k)
Where (h,k) represents the vertex of the parabola and 'a' is a constant. In this case, since the vertex is (0,-5), the equation becomes:
x² = 4a(y + 5)