Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -5}\frac{5 x^{2} + 60 x + 175}{- 5 x^{2} - 32 x - 35}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to -5}\frac{5 x^{2} + 60 x + 175}{- 5 x^{2} - 32 x - 35} = \lim_{x \to -5}\frac{10 x + 60}{- 10 x - 32} = \frac{10 (-5) + 60}{- 10 (-5) - 32} = \frac{5}{9}$