Provided $\lim _{x \rightarrow-1} f(x)=5$ and $\lim _{x \rightarrow-1} g(x)=8$. Compute the following limits: A) $\lim _{x \rightarrow-1}(f(x))^{3}+g(x)=$ B) $\lim _{x \rightarrow-1}\left[\frac{25 f(x)}{f(x)-g(x)}\right]=$ C) $\lim _{x \rightarrow-1} \sqrt{25 f(x)+g(x)}=$ D) $\lim _{x \rightarrow-1} \frac{f(x)}{[f(x)+g(x)]^{2}}=$

Step 1 ：Given that \(\lim _{x \rightarrow-1} f(x)=5\) and \(\lim _{x \rightarrow-1} g(x)=8\)

Step 2 ：We need to find the limit of \((f(x))^3 + g(x)\) as x approaches -1

Step 3 ：The limit of a sum is the sum of the limits, so we can find the limit of each part separately and then add them together

Step 4 ：The limit of \((f(x))^3\) as x approaches -1 is \((\lim_{x \rightarrow -1} f(x))^3 = 5^3 = 125\)

Step 5 ：The limit of \(g(x)\) as x approaches -1 is \(\lim_{x \rightarrow -1} g(x) = 8\)

Step 6 ：So the limit of the whole expression is \(125 + 8 = 133\)

Step 7 ：Final Answer: The limit of \((f(x))^3 + g(x)\) as \(x\) approaches -1 is \(\boxed{133}\)