To simplify this expression, we first need to evaluate the terms within the parentheses before performing the division.

1/2 - 1/3 = 3/6 - 2/6 = 1/6

Now, the expression becomes:

(4 + 1) / (1/6) : (4 - 1) / (1/6)

Simplify further:

5 / (1/6) : 3 / (1/6)

Now, we need to divide 5 by 1/6 and 3 by 1/6:

5 / (1/6) = 5 (6/1) = 30
3 / (1/6) = 3 (6/1) = 18

Finally, the expression simplifies to:

30 : 18

Which further simplifies to:

5 : 3

Therefore, (4 + 1:(1/2 - 1/3)):(4 - 1:(1/2 - 1/3)) simplifies to 5:3.