Find five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$.

Since we want to find five rational numbers between the given numbers, multiplying the numerator and denominator of the above numbers by 5 + 1 i.e. by 6, we get $\dfrac{18}{30}$ and $\dfrac{24}{30}$, which are equivalent to the given numbers.

$\text{As } 18 \lt 19 \lt 20 \lt 21 \lt 22 \lt 23 \lt 24, \\[0.7em] \dfrac{18}{30} \lt \dfrac{19}{30} \lt \dfrac{20}{30} \lt \dfrac{21}{30} \lt \dfrac{22}{30} \lt \dfrac{23}{30} \lt \dfrac{24}{30} \\[0.7em] \Rightarrow \dfrac{3}{5} \lt \dfrac{19}{30} \lt \dfrac{2}{3} \lt \dfrac{7}{10} \lt \dfrac{11}{15} \lt \dfrac{23}{30} \lt \dfrac{4}{5}$

Therefore, six rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are:

$\bold{\dfrac{19}{30}}, \bold{\dfrac{2}{3}}, \bold{\dfrac{7}{10}}, \bold{\dfrac{11}{15}}, \bold{\dfrac{23}{30}}$