1. Stating the problem: Simplify the expression $$\frac{8mn}{3} \div \frac{4mn^2}{5}$$ and choose the correct option. 2. Recall the rule for division of fractions: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$. 3. Apply the rule to the problem: $$\frac{8mn}{3} \times \frac{5}{4mn^2}$$ 4. Multiply numerators and denominators: $$\frac{8mn \times 5}{3 \times 4mn^2} = \frac{40mn}{12mn^2}$$ 5. Simplify the fraction by canceling common factors: $$\frac{\cancel{40}^{{10} \times 4} \cancel{m} \cancel{n}}{\cancel{12}^{3 \times 4} \cancel{m} n^2} = \frac{10}{3n}$$ 6. Explanation: We canceled $m$ and one $n$ from numerator and denominator. The remaining $n$ in denominator stays. 7. Final answer: $$\frac{10}{3n}$$ which corresponds to option A.