1. **State the problem:** Simplify the expression $$\frac{5x^2}{20x^4 - 120x^3}$$. 2. **Factor the denominator:** Factor out the greatest common factor (GCF) from the denominator. $$20x^4 - 120x^3 = 20x^3(x - 6)$$ 3. **Rewrite the expression:** $$\frac{5x^2}{20x^3(x - 6)}$$ 4. **Simplify the fraction:** Divide numerator and denominator by the common factor $5x^2$. $$\frac{\cancel{5x^2}}{\cancel{5x^2} \cdot 4x (x - 6)} = \frac{1}{4x(x - 6)}$$ 5. **Final simplified form:** $$\boxed{\frac{1}{4x(x - 6)}}$$ This means the original expression simplifies to $\frac{1}{4x(x - 6)}$ where $x \neq 0$ and $x \neq 6$ to avoid division by zero.