To find 5 rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$, we convert them into equivalent fractions with a larger denominator. Since we need 5 numbers, we multiply both fractions by 6 (5 + 1).

Step 1: $\frac{2}{5} \times \frac{6}{6} = \frac{12}{30}$ and $\frac{3}{5} \times \frac{6}{6} = \frac{18}{30}$.

Step 2: Identify 5 integers between 12 and 18, which are 13, 14, 15, 16, and 17. Since there are infinitely many rational numbers between any two points, we can easily find these.

Step 3: The 5 rational numbers are $\frac{13}{30}$, $\frac{14}{30}$, $\frac{15}{30}$, $\frac{16}{30}$, and $\frac{17}{30}$.