f(x) is a parabola with vertex at the origin (0,0).
The vertex of g(x) has to be at (-5,-3) because the 5 units to the left means 0-5=-5 (x coord); and 3 units down means 0-3=-3 (y coord).
Therefore g(x)=(x+5)2-3 (when x=-5, y=-3 which puts the vertex at (-5,-3)).