The focus of a parabola is (−5,−1) and the directrix is y=−3.
what is an equation of the parabola?
(x+5)² = 2(y + 5)
(x+5)² = y + 2
(x+5)² = 4(y + 2)
(x+5)² = 8(y + 5)
explain your answer , you

the equation for a parabola with focus (h, k+p) and directrix y=k-p is 


so using your directrix y=-3, and knowing directrix is y=k-p, you have 
-3=k-p.
similarly, knowing the focus is defined by (h,k+p) and your focus is (-5,-1)
you have the equation -1=k+p.

you now have a system of equations

which you can solve using any method, I will use elimination.
adding down

you now have k and can find p using either equation. 
.

now you plug those in, getting the answer