Answer
$-2$
Work Step by Step
Factor each polynomial:
$$\lim_{x\to -1}\frac{x^2-4x-5}{x^3+1}\\=\lim_{x\to -1}\frac{(x+1)(x-5)}{(x+1)(x^2-x+1)}.$$
Cancel the common factors: $$\lim_{x\to -1}\frac{x-5}{x^2-x+1}\\=\frac{(-1)-5}{((-1)^2-(-1)+1)}\\=\frac{(-6)}{1+1+1}\\=-2$$
