The simple answer is: if box 5, of the 1098-T is more than box 1, the difference is the taxable scholarship amount. Taxable scholarship, including Pell grants, is the amount of the scholarship that exceeds qualified educational expenses (QEE-tuition, fees and undergraduate course materials). So, the difference between box 5 and box 1 can be reduced by other QEE, not shown in box 1, like books.
If box 1 is more than box 5, none is taxable.
There is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his (your joint) return. That way, you can claim the tuition credit on your joint return. You 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 an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and you can not claim the American opportunity credit. But if she reports $6000 as income on your return, then you can claim $4000 of qualified expenses for the tuition credit.
