1. **State the problem:** We need to calculate $20 \div \frac{5}{7}$ and simplify the answer. 2. **Recall the rule for division of fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. 3. **Apply the rule:** $$20 \div \frac{5}{7} = 20 \times \frac{7}{5}$$ 4. **Multiply the numbers:** $$20 \times \frac{7}{5} = \frac{20 \times 7}{5}$$ 5. **Simplify the fraction:** $$\frac{20 \times 7}{5} = \frac{\cancel{20}^4 \times 7}{\cancel{5}^1} = 4 \times 7 = 28$$ 6. **Final answer:** $$28$$ The simplest form of $20 \div \frac{5}{7}$ is $28$.