Answer
$(y+2)^2=8(x-5)$
Work Step by Step
General form of a horizontal parabola is given as: $(y-k)^2=4p(x-k)$...(1)
Here, $\text{Vertex}=(h,k)$ and focus is: $(h+p, k)$
As we are given $\text{Vertex}=(5,-2)$ and focus is: $(7,-2)$
Thus, $h=5,k=-2$ and $h+p=7 \implies 5+p=7$
or, $p=2$
From equation (1), we have $(y-(-2))^2=4(2)(x-5)$
or, $(y+2)^2=8(x-5)$
