Answer
See explanations.
Work Step by Step
Step 1. To prove the limit $\lim_{x\to-5}\frac{1}{(x+5)^2}=\infty$, for any large positive number $B$, we need to find a corresponding value $\delta\gt0$ so that for all x in the interval $0\lt|x+5|\lt\delta$, we get $\frac{1}{(x+5)^2}\gt B$
Step 2. The last inequality $\frac{1}{(x+5)^2}\gt B$ gives $(x+5)^2\lt 1/B$ which leads to $|x+5|\lt1/ \sqrt B$, thus we can choose $\delta=1/\sqrt B$ and when we go back in the steps, for all x in the interval $0\lt|x+5|\lt\delta$, we get $\frac{1}{(x+5)^2}\gt B$ which proves the limit statement.