To solve this expression, we can simplify each term separately and then add them together.

First, let's simplify the first term: 5/8 * (-2/9)
To multiply fractions, we multiply the numerators together and the denominators together.
(5 * -2) / (8 * 9) = -10/72
Since -10/72 can be simplified further, we divide both the numerator and denominator by their greatest common divisor, which is 2.
-10/72 = -5/36

Next, let's simplify the second term: 5/8 * (-7/9)
(5 * -7) / (8 * 9) = -35/72

Lastly, let's simplify the third term: 1 1/3 * (-5/8)
To multiply a mixed number by a fraction, we first convert the mixed number to an improper fraction.
1 1/3 = (3 * 1 + 1) / 3 = 4/3
Then, we multiply the improper fraction by the fraction.
(4/3) * (-5/8) = -20/24
Since -20/24 can be simplified further, we divide both the numerator and denominator by their greatest common divisor, which is 4.
-20/24 = -5/6

Now, let's add all the simplified terms together:
-5/36 + -35/72 + -5/6
To add fractions, we need to have a common denominator. The least common multiple of 36, 72, and 6 is 72.
-5/36 = -10/72
-5/6 = -60/72
Now, we can add the fractions:
-10/72 + -35/72 + -60/72 = -105/72

Therefore, the expression 5/8 * (-2/9) + 5/8 * (-7/9) + 1 1/3 * (-5/8) simplifies to -105/72.