Solution:
There are infinite rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$
$\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$
$\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$
Therefore, rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are
$\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$