1. The problem is to calculate $15 \div \frac{9}{5}$ and express the answer as a fraction in lowest terms. 2. Dividing by a fraction is the same as multiplying by its reciprocal. So, $$15 \div \frac{9}{5} = 15 \times \frac{5}{9}$$ 3. Multiply the numerators and denominators: $$= \frac{15 \times 5}{9} = \frac{75}{9}$$ 4. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 75 and 9 is 3. $$\frac{75 \div 3}{9 \div 3} = \frac{25}{3}$$ 5. So, the answer as a fraction in lowest terms is: $$\boxed{\frac{25}{3}}$$