1. **State the problem:** Simplify the expression $\frac{3}{5x^2}$. 2. **Understand the expression:** This is a fraction where the numerator is 3 and the denominator is $5x^2$. 3. **No further simplification is possible:** Since 3 and $5x^2$ have no common factors, the expression is already in simplest form. 4. **Final answer:** $$\frac{3}{5x^2}$$