1. **State the problem:** Solve the equation $$\frac{1}{5} x^3 = 25$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x^3$ first by multiplying both sides by 5, then take the cube root of both sides. 3. **Isolate $x^3$:** $$\frac{1}{5} x^3 = 25$$ Multiply both sides by 5: $$\cancel{\frac{1}{5}} \times 5 \times x^3 = 25 \times 5$$ $$x^3 = 125$$ 4. **Take the cube root:** $$x = \sqrt[3]{125}$$ Since $125 = 5^3$, $$x = 5$$ 5. **Answer:** The solution is $x = 5$.