First thing: if you graduated this year it was probably your fifth calendar year of attending school Be sure you (or your parents) didn’t already claim the American Opportunity Credit (AOC) the maximum 4 times.
You can not claim the $5878 you paid in 2019 on your 2020 tax return. It had to be claimed on your 2019 return or not at all.
Fortunately there is a loop hole available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
Using your numbers : Student has $8687 in box 5 of the 1098-T and $7596 in box 1. At first glance he/she has $1091 of taxable income and nobody can claim the American opportunity credit. But if she reports $5091 as income on her return, the parents can claim $4000 of qualified expenses on their return for the AOC.
