Yes, basically. But it's not clear where the $5000 comes from. Was there suppose to b some info at "spoiler".
What is boxes 1 and 5 of her 1098-T. How much other expenses (books & a computer, but not room & board) does she have? What other income does she have? Id your tax liability $1500 or more (so that you get the full $2500 AOTC).
