1. **State the problem:** We want to find the value of $\frac{3}{5} - \frac{1}{3}$. 2. **Find a common denominator:** The denominators are 5 and 3. The least common denominator (LCD) is $5 \times 3 = 15$. 3. **Rewrite each fraction with the common denominator:** $$ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}, \quad \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} $$ 4. **Subtract the fractions:** $$ \frac{9}{15} - \frac{5}{15} = \frac{9 - 5}{15} = \frac{4}{15} $$ 5. **Final answer:** $$ \boxed{\frac{4}{15}} $$ This means $\frac{3}{5} - \frac{1}{3} = \frac{4}{15}$.