1. **Problem:** Find the limit $$\lim_{z \to 1} \frac{z^2 + 5}{z + 5}$$ 2. **Formula:** To find limits of rational functions, if direct substitution does not cause division by zero, substitute directly. 3. **Step:** Substitute $z=1$: $$\frac{1^2 + 5}{1 + 5} = \frac{1 + 5}{6} = \frac{6}{6} = 1$$ 4. **Answer:** The limit is $$1$$. Note: There are 10 distinct problems in the user's message, but per instructions, only the first problem is solved here.