To solve the expression \( 10 \div \frac{2}{5} \), you can rewrite the division of a fraction as multiplication by its reciprocal.
So,
\[ 10 \div \frac{2}{5} = 10 \times \frac{5}{2} \]
Now, calculate \( 10 \times \frac{5}{2} \):
\[ 10 \times \frac{5}{2} = \frac{10 \times 5}{2} = \frac{50}{2} = 25 \]
Thus, the quotient of \( 10 \div \frac{2}{5} \) is
\[ \boxed{25} \]