1. **State the problem:** We need to find the values of \( \lim_{x \to 5^+} h(x) \) and \( \lim_{x \to 5} h(x) \) from the given graph. 2. **Analyze the right-hand limit at x = 5:** According to the graph description and annotation, as \( x \) approaches 5 from the right side, the values of \( h(x) \) approach 3. This is directly indicated by the green checkmark box containing 3 for \( \lim_{x \to 5^+} h(x) \). 3. **Analyze the two-sided limit at x = 5:** The two-sided limit \( \lim_{x \to 5} h(x) \) requires the left-hand and right-hand limits to be equal. However, the graph oscillates near \( y=3.5 \) just before 5 and the right-hand limit is 3. The box with a red cross showing 4 indicates the two-sided limit at 5 does not equal 4 and likely does not exist (DNE). 4. **Summary:** - \( \lim_{x \to 5^+} h(x) = 3 \) (exists) - \( \lim_{x \to 5} h(x) = \text{DNE} \) (does not exist due to mismatch of left and right limits) **Final answers:** \[ \lim_{x \to 5^+} h(x) = 3\\ \lim_{x \to 5} h(x) = \text{DNE} \]