1. **State the problem:** Write the expression $\log_5 \left(\frac{1}{2}\right) + \log_5 50$ as a single logarithm and evaluate it. 2. **Recall the logarithm property:** The sum of logarithms with the same base can be combined using the product rule: $$\log_b A + \log_b B = \log_b (A \times B)$$ 3. **Apply the product rule:** $$\log_5 \left(\frac{1}{2}\right) + \log_5 50 = \log_5 \left(\frac{1}{2} \times 50\right)$$ 4. **Simplify the argument:** $$\frac{1}{2} \times 50 = 25$$ 5. **Rewrite the expression:** $$\log_5 25$$ 6. **Evaluate the logarithm:** Since $25 = 5^2$, $$\log_5 25 = \log_5 5^2 = 2$$ **Final answer:** $$\boxed{2}$$