Answer
True.
Work Step by Step
Given: $\lim\limits_{x \to 5} g(x) = 0$; $\lim\limits_{x \to 5} f(x) = 2$
$\lim\limits_{x \to 5} \frac{f(x)}{g(x)} = \frac{\lim\limits_{x \to 5} f(x)}{\lim\limits_{x \to 5} g(x)} = \frac{2}{0^{+}}$
So the limit does not exist.
