It looks like AP2 might be a better objective function/Set target cell. Some math/algebra before we get to programming:

1) AP2=ABS(AJ2/AK2)=ABS(AJ2/(AI2-AE2+AJ2)). You have not given any indication what is in AI2, but I would guess that it is some function of AE2.
2) At one extreme: AJ2=0, AP2 becomes ABS(0/AK2)=0
3) At the other extreme: AJ2=AE2, AP2 becomes ABS(AJ2/(AI2-AE2+AJ2))=ABS(AE2/AI2), which, I assume will always be greater than 5.

So, somewhere between AJ2=0 and AJ2=AE2, AP2 is equal to 5. Are you certain that there is only one possible value for AJ2 where AP2=5, or are there multiple possible values for AJ2 where AP2=5?

Here's how I would analyze the problem next:

4) Set AP2=5 and solve for AJ2 --- 5=ABS(AJ2/(AI2-AE2+AJ2)) This will probably involve two runs through, one where the denominator is positive and one where the denominator is negative (if the denominator can be both positive and negative, given the other constraints). If AI2 does not involve AJ2, then this should be fairly straightforward algebra, you will get one or two possible solutions for AJ2, choose the smaller. In this scenario, Solver is not even needed, since we found the solutions algebraically. You would only need to enter the appropriate formula into AJ2 at AP2=5.
4a) To be absolutely certain that this results in the desired solution, you may want to check what happens at AJ2 slightly larger than 0 or slightly less than AE2, and at other values for AJ2 to make sure that there are no surprises in the behavior of AP2.

I realize that this is all math and no programming so far, but this may yield easier programming solutions, once the math is understood.