The problem asks to find the limit of $f(x)$ as $x \to 5$ based on the given graph.

Steps to find the limit:

1. Observe the left-hand limit as $x \to 5^-$ (approaching 5 from the left):

   • The graph is moving downwards towards the point at $(5, -3)$, which suggests that $\lim_{x \to 5^-} f(x) = -3$.

2. Observe the right-hand limit as $x \to 5^+$ (approaching 5 from the right):

   • The graph is also approaching the same point $(5, -3)$. Thus, $\lim_{x \to 5^+} f(x) = -3$.

3. Since both the left-hand and right-hand limits as $x \to 5$ are equal, the overall limit exists and is equal to -3.

Final answer:

$\lim_{x \to 5} f(x) = -3$

Therefore, the correct choice is -3.

Would you like further details or explanations? Here are five related questions you can explore:

1. How do you calculate a limit if the function has a discontinuity?
2. What is the difference between a left-hand limit and a right-hand limit?
3. How can a limit not exist even if both one-sided limits are defined?
4. What is the role of the limit in understanding function behavior near discontinuities?
5. How does the definition of a limit relate to continuity?

Tip: When solving limits graphically, always check both sides (left and right) to ensure consistency.