Find 5 rational numbers between $\dfrac{2}{5}$ and $\dfrac{3}{5}$.

Given,

Two rational numbers : $\dfrac{2}{5}$ and $\dfrac{3}{5}$.

Multiplying numerator and denominator by 6 :

$\Rightarrow \dfrac{2}{5} = \dfrac{2 \times 6}{5 \times 6} = \dfrac{12}{30} \\[1em] \Rightarrow \dfrac{3}{5} = \dfrac{3 \times 6}{5 \times 6} = \dfrac{18}{30}.$

So, the 5 rational numbers between $\dfrac{12}{30}$ and $\dfrac{18}{30}$ are :

$\Rightarrow \dfrac{13}{30}, \dfrac{14}{30}, \dfrac{15}{30}, \dfrac{16}{30}, \dfrac{17}{30} \\[1em] \Rightarrow \dfrac{13}{30}, \dfrac{7}{15}, \dfrac{1}{2}, \dfrac{8}{15}, \dfrac{17}{30}.$

Hence, 5 rational numbers between $\dfrac{2}{5}$ and $\dfrac{3}{5}$ are $\dfrac{13}{30}, \dfrac{7}{15}, \dfrac{1}{2}, \dfrac{8}{15}$ and $\dfrac{17}{30}$.