Identify the vertex of the parabola. \[ f(x)=-5(x+5)^{2}-7 \]

Step 1 ：Identify the vertex of the parabola. The equation is given as \(f(x)=-5(x+5)^{2}-7\).

Step 2 ：The vertex of a parabola given in the form \(f(x) = a(x-h)^2 + k\) is at the point (h, k).

Step 3 ：In this case, the equation is already in that form, so we can directly read off the vertex.

Step 4 ：From the equation, h = -5 and k = -7.

Step 5 ：So, the vertex = (-5, -7).

Step 6 ：\(\boxed{\text{The vertex of the parabola is } (-5, -7)}\)