LCM of 2,3 is 6.
We shall make same denominator.
3/2 = 3x3/(2x3) =9/6
5/3 = 5x2/(3x2) = 10/6
Now multiply both numerator and denominator with 6.
9/6 = 9x6/(6x6) = 54/36
10/6 = 10x6/(6x6) = 60/36
55/60, 56/60, 57/60, 58/60, 59/60 are five rational numbers between 3/2 and 5/3.