Question

find the focus of the parabola (x-5)^2=8(y+4)

Answer 1

well, keeping in mind that the "focus form of a parabola" is
=> \(\bf (x-h)^2=4p(y-k); \pm p\)
p = distance of the focus from the (h, k) vertex
now look at your equation
=> \(\bf x-5)^2=8(y+4)\)
you're pretty much given the (h, k) of the parabola
it has an squared "x" component, so it's opening vertically
the "4P" term is positive, so that means is opening upwards over the y-axis

Answer 2

if you want the "p" distance, well
4P = 8
solve for "p"