To solve for x, we first need to simplify the equation:

4x + 5 = (8/9) / 13

First, let's simplify the right side of the equation:

(8/9) / 13 = 8/9 * 1/13 = 8/117

Now, the equation becomes:

4x + 5 = 8/117

Next, we'll isolate the variable x by subtracting 5 from both sides:

4x = 8/117 - 5
4x = 8/117 - 585/117
4x = -577/117

Finally, to solve for x, divide both sides by 4:

x = -577/468 = - 577/468

Therefore, x = -577/468.