1. **State the problem:** Simplify the expression $\log_5 7 + \log_5 8 - \log_5 6$. 2. **Recall the logarithm properties:** - $\log_b a + \log_b c = \log_b (a \times c)$ - $\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)$ 3. **Apply the addition property:** $\log_5 7 + \log_5 8 = \log_5 (7 \times 8) = \log_5 56$ 4. **Apply the subtraction property:** $\log_5 56 - \log_5 6 = \log_5 \left(\frac{56}{6}\right)$ 5. **Simplify the fraction:** $\log_5 \left(\frac{\cancel{56}}{\cancel{6}}\right) = \log_5 \frac{28}{3}$ 6. **Final answer:** $\boxed{\log_5 \frac{28}{3}}$