So, looks like you're doing everything possible to continue to confuse yourself. Keep it up, and you'll think yourself right into the asylum. 🙂
I am 100% certain that the $7590 went directly to the school.
That's not what is in question here. What's in question is, are you 100% certain the 529 distribution that went to the school, is included in box 5 of the 1098-T?
With only a $25 difference, Assuming you see the 529 distribution as a separate line item on the student's financial printout, I'm 100% certain it's included in box 5 of the 1098-T, based on your math.
Box 5 of the 1098-T only includes income received by the school from third party sources. Third party sources would income scholarships, grants, and anything else the school received *directly* from a 3rd party.
So if the 529 was paid directly to the school by the 529 plan administrator, that would be 3rd party income to the school, as far as the school is concerned since neither you or the student never had control of that money, or even laid a physical finger on that money before the school got it.
Whereas box 1 of the 1098-T is the amount paid to the school from "all" sources, including the amount in box 5.
Since box 5 is smaller than box 1, if you subtract box 5 from box 1, the difference is what was paid in cash by you and/or the student. That cash payment amount is what was paid to the school "out of pocket" and that amount is what will qualify you for the AOTC any any other education tax breaks you may qualify for.
