Answer
$(x-2)^2=-8(y+3)$
Work Step by Step
General form of a vertical parabola is given as: $(x-h)^2=4p(y-k)$...(1)
Here, $\text{Vertex}=(h,k)$ and focus is: $(h, k+p)$
As we are given $\text{Vertex}=(2,-3)$ and focus is: $(2,-5)$
Thus, $h=2,k=-3$ and $k+p=-5 \implies -3+p=-5$
or, $p=-2$
From equation (1), we have $(x-2)^2=4(-2)(y-(-3))$
or, $(x-2)^2=-8(y+3)$
