To find the product of the fractions \( \frac{2}{3} \) and \( \frac{1}{5} \), you multiply the numerators together and the denominators together:
\[ \frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15} \]
Therefore, the answer is \( \frac{2}{15} \).