Q. Do I remove the 1098T from my tax return?
A. No. You modify it when you enter it. In your case, enter the 1098-T with $4000 in box 1 and box 5 blank.
The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. The easiest way to do this is just change the numbers in boxes 1& 5 to what your records show. The 1098-T that you enter in TT is not sent to the IRS.
Q. Does my son also put the 1098-T on his tax return?
A. Yes, but he also modifies the numbers. Because you used $4000 of the tuition on your return, he enters only $1784 ($5784 - 4000 = 1784) in box 1, on his return (or, as Bsch4477 describes, add $4000 to box 5, instead of subtracting $4000 from box 1).
Q. Will that make him owe money?
A. Yes. Only scholarships that are allocated to qualified expenses (tuition, fees, books and other course materials, including a required computer) are tax free. Room & board are not qualified expenses.
Restating what @Bsch4477 said earlier:
There is a tax “loop hole” available to claim an education credit, for the parents of students on scholarship. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), 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 as an example: Student has $17,502 in box 5 of the 1098-T and $5784 in box 1. At first glance he has $11,718 of taxable income and nobody can claim the American opportunity credit. But if he reports $15,718 as income on his return, the parents can claim $4000 of qualified expenses on their return. The student will get a $13,850 standard deduction, so only $1868 (15718 - 13850 = 1868) will actually get taxed.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1000 in expenses for those course materials, paid out of pocket, he would only need to report $14,718 of taxable scholarship income, instead of $15,718.
The IRS actually encourages use of this technique. From the form 1040 instructions: “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040 and IRS.gov/EdCredit". PUB 970 even has examples of how to do the “loop hole”.
