To multiply the fractions \( \frac{2}{5} \) and \( \frac{5}{6} \), you multiply the numerators together and the denominators together:
\[ \frac{2}{5} \times \frac{5}{6} = \frac{2 \times 5}{5 \times 6} = \frac{10}{30} \]
Next, we simplify \( \frac{10}{30} \) by finding the greatest common divisor (GCD) of 10 and 30, which is 10:
\[ \frac{10 \div 10}{30 \div 10} = \frac{1}{3} \]
Thus, the product in simplest form is:
\[ \frac{1}{3} \]