https://file.aiquickdraw.com/mathbot/file/1725984031342g8aeshdq.jpg

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**.

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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.

Use the graph of f(x) to find the limit as x approaches 5. If the limit does not exist, explain why.

Determine the limit of the function f(x) as x approaches 5 using graphical interpretation. This problem involves key concepts such as one-sided limits and checking continuity. Suitable for high school students (Grades 10-12).

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