To solve this expression, we need to simplify each set of parentheses separately and then subtract the results.

First, let's simplify the first set of parentheses: (6-2/3+1/2)

To add or subtract fractions, we need a common denominator. The common denominator for 3 and 2 is 6.

(6-2/3+1/2) = (6*6 - 2*2 + 1*3) / 6 = (36 - 4 + 3) / 6 = 35/6

Next, let's simplify the second set of parentheses: (5+5/3-3/2)

To add or subtract fractions, we need a common denominator. The common denominator for 3 and 2 is 6.

(5+5/3-3/2) = (5*6 + 5*2 - 3*3) / 6 = (30 + 10 - 9) / 6 = 31/6

Finally, let's simplify the third set of parentheses: (3-7/3+5/2)

To add or subtract fractions, we need a common denominator. The common denominator for 3 and 2 is 6.

(3-7/3+5/2) = (3*6 - 7*2 + 5*3) / 6 = (18 - 14 + 15) / 6 = 19/6

Now, let's subtract the results:

(35/6) - (31/6) - (19/6) = (35 - 31 - 19) / 6 = -15/6

Therefore, the final result is -15/6, which can be simplified to -5/2.