1. Stating the problem: Calculate $\frac{5}{6} \div \frac{2}{5}$. 2. Formula: Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. Apply the formula: $$\frac{5}{6} \div \frac{2}{5} = \frac{5}{6} \times \frac{5}{2}$$ 4. Multiply numerators and denominators: $$\frac{5 \times 5}{6 \times 2} = \frac{25}{12}$$ 5. Simplify if possible: $\frac{25}{12}$ is an improper fraction and cannot be simplified further. 6. Convert to mixed number: $$25 \div 12 = 2 \text{ remainder } 1$$ So, $$\frac{25}{12} = 2 \frac{1}{12}$$ Final answer: $\boxed{\frac{25}{12} \text{ or } 2 \frac{1}{12}}$