42 1/2(19/18-5/9)-5 2/5*5/9

First, let's simplify the expression inside the parentheses:

19/18 - 5/9 = (29 + 1)/18 - (52)/18
= (18 + 1)/18 - 10/18
= 19/18 - 10/18
= 9/18
= 1/2

Now, we substitute this back into the original expression:

42 1/2(1/2) - 5 2/55/9
= 4(5/2) 1/2 - 27/5 5/9
= 10 * 1/2 - 27/9
= 5 - 3
= 2

Therefore, the final answer is 2.