To simplify the expression, we can combine like terms.

First, let's combine the terms with x:

4/9x + 4/9x = (4/9 + 4/9)x = (8/9)x

Next, let's combine the constant terms:

-2/3 - 1/3 + 5 = (-2/3 - 1/3) + 5 = (-3/3) + 5 = 2 + 5 = 7

Now, the expression becomes:

(8/9)x + 7 + 5 4/9

To add the mixed number, we need to convert it to an improper fraction:

5 4/9 = (9 * 5 + 4)/9 = 49/9

Now, the expression becomes:

(8/9)x + 7 + 49/9

To add the fractions, we need a common denominator. The least common multiple of 9 and 9 is 9.

So, we can rewrite the expression as:

(8/9)x + 7 + (49/9)(9/9) = (8/9)x + 7 + 441/9

Now, we can combine the fractions:

(8/9)x + 7 + 441/9 = (8/9)x + 7 + 49

Finally, the simplified expression is:

(8/9)x + 49 + 7 = (8/9)x + 56