1. **State the problem:** We need to estimate the limit \(\lim_{x\to -5} h(x)\) based on the graph described. 2. **Analyze the graph near \(x = -5\):** The graph has a U-shaped curve with an open circle at \(x = -5\) just below \(y=2\), and a closed circle at \(x = -5\) just above the x-axis (near \(y=0.2\)). 3. **Recall the definition of limit:** The limit \(\lim_{x\to a} f(x)\) is the value \(f(x)\) approaches as \(x\) gets close to \(a\), regardless of the function's value at \(a\). 4. **Check left and right behavior:** Since the curve approaches the open circle near \(y=1.3\) (approximately) from both sides of \(x=-5\), the limit should be around 1.3, the height of the open circle, not the closed circle. 5. **Interpret closed and open circles:** The closed circle represents \(h(-5)\) (the actual function value), while the limit depends on the curve (open circle). Thus, the limit is approximately 1.3. 6. **Conclusion:** The reasonable estimate is \(\lim_{x\to -5} h(x) = 1.3\). **Final answer:** Choice C: \(1.3\).