1. **Problem Statement:** Find the limit of the function $f(x)$ as $x$ approaches $-5$. 2. **Understanding Limits:** The limit $\lim_{x \to a} f(x)$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both sides. 3. **From the graph description:** At $x = -5$, the function sharply falls to near $-5$ on the $y$-axis. 4. **Evaluating the limit:** Since the function approaches $-5$ from both sides near $x = -5$, we have $$\lim_{x \to -5} f(x) = -5.$$