Answer
See explanations.
Work Step by Step
Since the question did not specify that $f, g, h$ are continuous functions, it is possible that $f(2), g(2), h(2)$ have values other than $-5$ or even do not exist. While it is possible that $f(2)=0$, it is not possible that $\lim\limits_{x \to 2}f(x)=0$ since this will violate the Sandwich Theorem. The correct value is $\lim\limits_{x \to 2}f(x)=-5$
