1. **State the problem:** We need to calculate $15 \div \frac{1}{5}$. This means dividing 15 by the fraction one-fifth. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{5}$ is $5$. 3. **Apply the rule:** $$15 \div \frac{1}{5} = 15 \times 5$$ 4. **Calculate the multiplication:** $$15 \times 5 = 75$$ 5. **Final answer:** $$15 \div \frac{1}{5} = 75$$ This means 15 divided by one-fifth equals 75.