For the given functions $f$ and $g$, find the indicated composition.
\[
\begin{array}{l}
f(x)=x^{2}-2 x-5, \quad g(x)=x^{2}+2 x+2 \\
(f \circ g)(-4)
\end{array}
\]
$(f \circ g)(-4)$
(A) 394
B) 336
C) 133
(D) 75

Step 1 ：Find the composition of the functions: \(f(g(x))\)

Step 2 ：\(f(g(x)) = f(x^2 + 2x + 2)\)

Step 3 ：\(f(g(x)) = (x^2 + 2x + 2)^2 - 2(x^2 + 2x + 2) - 5\)

Step 4 ：Substitute \(x = -4\) into the composed function: \(f(g(-4))\)

Step 5 ：\(f(g(-4)) = ((-4)^2 + 2(-4) + 2)^2 - 2((-4)^2 + 2(-4) + 2) - 5\)

Step 6 ：\(f(g(-4)) = (16 - 8 + 2)^2 - 2(16 - 8 + 2) - 5\)

Step 7 ：\(f(g(-4)) = (10)^2 - 2(10) - 5\)

Step 8 ：\(f(g(-4)) = 100 - 20 - 5\)

Step 9 ：\(f(g(-4)) = 75\)

Step 10 ：\(\boxed{75}\)