1. We are asked to find the limit of the function $f(x)$ as $x$ approaches $-5$. 2. The limit of a function at a point $a$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both sides. 3. From the graph description, near $x = -5$, there is an open circle at $(-5, -2)$, meaning $f(-5)$ is not defined or is different from the limit. 4. The graph approaches the value $-2$ from both sides as $x$ approaches $-5$. 5. Therefore, $$\lim_{x \to -5} f(x) = -2.$$