Answer
$-10$
Work Step by Step
Consider: $\lim\limits_{x \to -5}f(x)=\lim\limits_{x \to -5}\dfrac{x^2-25}{x +5}$
Now, $f(-5)=\dfrac{(-5)^2 -25}{-5+5}=\dfrac{0}{0}$
The limit shows an indeterminate form. Thus, apply L-Hospital's rule: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$
Thus:
$\lim\limits_{x \to -5}\dfrac{2x}{1}=2(-5)=-10$
