To solve this problem, we need to multiply the fractions and then add the results.

First, let's simplify the fractions:

5/9 13/28 = 65/252
13/28 4/9 = 1/3

Now, add the simplified fractions:

65/252 + 1/3

To find a common denominator for 252 and 3, we can multiply 252 by 3 to get 756.

(65 3)/(252 3) + 252/756
195/756 + 252/756

Now we can add the fractions:

(195 + 252)/756
447/756

So, 5/9 13/28 + 13/28 4/9 = 447/756.