1. **State the problem:** We need to evaluate the division of two fractions: $$\frac{5}{4} \div \frac{3}{5}$$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its reciprocal. The reciprocal of $$\frac{3}{5}$$ is $$\frac{5}{3}$$. 3. **Apply the rule:** $$\frac{5}{4} \div \frac{3}{5} = \frac{5}{4} \times \frac{5}{3}$$ 4. **Multiply the numerators and denominators:** $$\frac{5 \times 5}{4 \times 3} = \frac{25}{12}$$ 5. **Simplify if possible:** $$\frac{25}{12}$$ is an improper fraction and cannot be simplified further. 6. **Convert to mixed number (optional):** $$\frac{25}{12} = 2 \frac{1}{12}$$ **Final answer:** $$\frac{25}{12}$$ or $$2 \frac{1}{12}$$.