1. **State the problem:** Simplify the expression $$\frac{5x}{2y} \div \frac{3x}{4y}$$. 2. **Recall the rule for division of fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{5x}{2y} \div \frac{3x}{4y} = \frac{5x}{2y} \times \frac{4y}{3x}$$. 3. **Multiply the numerators and denominators:** $$= \frac{5x \times 4y}{2y \times 3x} = \frac{20xy}{6xy}$$. 4. **Simplify the fraction:** Since $xy$ appears in both numerator and denominator, they cancel out: $$= \frac{20}{6}$$. 5. **Reduce the fraction to simplest form:** Divide numerator and denominator by their greatest common divisor, 2: $$= \frac{10}{3}$$. **Final answer:** $$\frac{10}{3}$$. This corresponds to option A.