This calculation can be simplified as follows:

5(4.5+1 5/6)2/3 = 5(9/2 + 11/6)2/3
= 5(27/6 + 22/6)2/3
= 5(49/6)2/3
= (245/6)*2/3
= 490/6/3
= 490/18
= 27 1/18

So, 5(4.5+1 5/6)2/3 is equal to 27 1/18.