Find 5 rational numbers between $\dfrac{1}{6}$ and $\dfrac{2}{5}$.

Given,

Two rational numbers : $\dfrac{1}{6}$ and $\dfrac{2}{5}$.

L.C.M. of 6 and 5 = 30.

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

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

$\Rightarrow \dfrac{6}{30}, \dfrac{7}{30}, \dfrac{8}{30}, \dfrac{9}{30}, \dfrac{10}{30} \\[1em] \Rightarrow \dfrac{1}{5}, \dfrac{7}{30}, \dfrac{4}{15}, \dfrac{3}{10}, \dfrac{1}{3}.$

Hence, 5 rational numbers between $\dfrac{1}{6}$ and $\dfrac{2}{5}$ are $\dfrac{1}{5}, \dfrac{7}{30}, \dfrac{4}{15}, \dfrac{3}{10}$ and $\dfrac{1}{3}$.