Write five rational numbers between $-\dfrac{3}{2}$ and $\dfrac{5}{3}$

LCM of 2 and 3 is 2 x 3 = 6

Make denominator of each given rational number equal to 6 (the LCM).

$-\dfrac{3}{2} = -\dfrac{3 \times 3}{2 \times 3} = -\dfrac{9}{6}$

and

$\dfrac{5}{3} = \dfrac{5 \times 2}{3 \times 2} = \dfrac{10}{6}$

The rational number between $-\dfrac{9}{6}$ and $\dfrac{10}{6}$ are $-\dfrac{8}{6}, -\dfrac{7}{6}, -\dfrac{6}{6}, -\dfrac{5}{6}, -\dfrac{4}{6}, -\dfrac{3}{6}, -\dfrac{2}{6}, -\dfrac{1}{6}, \dfrac{0}{6}, \dfrac{1}{6}, \dfrac{2}{6}, \dfrac{3}{6}, \dfrac{4}{6}, \dfrac{5}{6}, \dfrac{6}{6}, \dfrac{7}{6}, \dfrac{8}{6}, \dfrac{9}{6}$

From these rational numbers we can take any five rational number.

Hence, required rational numbers between $-\dfrac{3}{2}$ and $\dfrac{5}{3}$ are :

$-\dfrac{8}{6} , -\dfrac{6}{6} , -\dfrac{4}{6} , -\dfrac{2}{6} , \dfrac{2}{6}$

= $-\dfrac{4}{3} , -\dfrac{1}{1} , -\dfrac{2}{3} , -\dfrac{1}{3} , \dfrac{1}{3}$

Hence, $-1\dfrac{1}{3} , -1 , -\dfrac{2}{3} , -\dfrac{1}{3}$ and $\dfrac{1}{3}$ lies between $-\dfrac{3}{2}$ and $\dfrac{5}{3}$.