1. The problem is to simplify the expression $\log_p(8p^5)$. 2. Recall the logarithm product rule: $\log_b(xy) = \log_b(x) + \log_b(y)$. 3. Apply the product rule: $$\log_p(8p^5) = \log_p(8) + \log_p(p^5)$$ 4. Use the power rule of logarithms: $\log_b(a^c) = c \log_b(a)$. 5. Simplify $\log_p(p^5)$: $$\log_p(p^5) = 5 \log_p(p) = 5 \times 1 = 5$$ 6. So the expression becomes: $$\log_p(8) + 5$$ 7. Since $\log_p(8)$ cannot be simplified further without knowing $p$, the final simplified form is: $$\log_p(8) + 5$$