The directrix is always perpendicular to the parabola's axis of symmetry, so y=-1 is horizontal, meaning that the parabola is upright and has the general form y-k=a(x-h)2 where (h,k) is the vertex. In this case the vertex is (-5,2).
Therefore, y=a(x+5)2+2. We find a through the directrix line, which is as far from the vertex as the focus, which lies inside the arms of the parabola. Since the y-coordinate of the vertex is 2, this distance is 2-(-1)=2+1=3. The focal distance f=1/(4a). So 3=1/(4a) and 4a=⅓, making a=1/12. The directrix, in this case, is lower than the vertex so the focus is higher than the vertex and lies on the axis of symmetry (x=-5). The focus is therefore at (-5,5).
The equation of the parabola is y=(1/12)(x+5)2+2. This can be rewritten:
12y=x2+10x+25+24=x2+10x+49.