Calculate the total electric flux leaving the cubical surface formed by the six planes x, y, z = ±5 if the charge distribution is: (a) twopoint charges, 0.1 μc at (1,− 2, 3) and 17μc at (−1, 2,−2)

If I correctly recall my E&M studies from 1958,
I suspect that this is a chump question.

The E flux through ANY closed surface is equal to the net
charge inside, or maybe it's the net charge divided by  ε₀ .
Yep, I think that's it.

Your charges are both positive, so if they're inside your cube,
the net charge inside will be  17.1μC .

Your cube has all faces 5 units from the axes, and neither charge
has an x, y, or z component with absolute value greater or equal
to 5.  So both charges are well inside the cube.

Seems to me, then, like the total E flux through the cubical
surface is

                       17.1μC  / ε₀  .

I don't really care whether this is helpful or not. 
I just hope it's correct.