1. **State the problem:** Solve for $p$ in the equation $p^3 = 125$. 2. **Formula and rules:** To solve for $p$ when $p$ is raised to a power, use the inverse operation, which is taking the root. Here, since $p$ is cubed, take the cube root of both sides. 3. **Apply the cube root:** $$p = \sqrt[3]{125}$$ 4. **Evaluate the cube root:** Since $125 = 5^3$, we have $$p = \sqrt[3]{5^3}$$ 5. **Simplify:** $$p = 5$$ 6. **Answer:** The solution to $p^3 = 125$ is $p = 5$.