The parabola lies horizontally because the directrix is vertical. 4p(x-h)=(y-k)^2 where (h,k) is the vertex and p is the distance of the focus and directrix line from the curve. The vertex lies midway between the focus and directrix. The x-coord of the vertex is (-5-7)/2=-6, so h=-6. The focus lies on the line of symmetry, which must therefore be y=9, therefore k=9. The value of p=1 because the distance between the focus and directrix is 2p=-5-(-7)=2.
The vertex is at (-6,9) and the equation is 4(x+6)=(y-9)^2.