I am assuming you are claiming your daughter as a depedent?
What you want to determine for the credit is the total expenses paid in 2017. You possibly paid for Spring (Jan, Feb, March) 2017 but this might have been on last years 2016 1098-T . I do not know if this is her first year of school. But the rules are clear, what ever qualifying expenses were paid in 2017, will be used to calculate the credit.
1098-T will only include qualified education amounts in box 2. It will not include room and board and other non-qualified expenses. Do you know if some of her scholarships were for room and board? If so, that would explain why there is more money in box 5 than box 2. (Box 2 should not include non-qualifying expenses)
So yes I guess you have to go through school statements to get what was paid (either by you or with scholarships) in 2017. You will still probably have to include additional out of pocket expenses for books.
Next, you need to know the character of the scholarships. If some were for room and board, these will be taxable (probably to your daughter) because room and board are not qualifying expenses.
So if you have For Example $10,000 of qualifying tuition and $12,000 of scholarships (unrestricted), and $5000 room and board, we will apply $5000 of scholarship income to pay room and board $5000. That leaves $7000 scholarships and $10,000 tuition expenses. The credit would be computed on $3000., left over qualifying expenses.
Since there is excess scholarship money or (scholarship money that paid non-qualifying expenses The scholarships ($5000) in my example these will be reported on your daughter's tax return. If that is your daughter's only income, she will not be required to file a returnuntil she has income over $6350.
I am attaching additional explanation below that comes from Turbo Tax program "Is there a way to increase my credit"
Is there a way to increase my credit? From Turbo Tax on Demand Guidance
If you qualify for an education credit, the amount of credit you receive is based upon the total qualified education expenses you have. Tax free assistance, such as scholarships and grants, reduce your qualified expenses and, in turn, the amount of education credit you may receive. You may be able to increase an education credit if you choose to apply certain scholarships and grants against unqualified expenses (such as room and board) and reduce them instead. The new allocation will include that tax free assistance in income. However, the possible larger education credit may more than offset any tax due on the increased income.
Note: The terms of the scholarship or grant must allow it to be used for expenses other than qualified education expenses (such as room and board) to use this potential tax saving technique.
Example: Danielle had $5,000 of tuition expenses and $4,000 of room and board for fall 2017 when she went to college. She received a $5,000 grant in which the terms did not restrict its usage. Her parents paid the remainder of Danielle's expenses and claimed her as a dependent. If the grant is used to offset her tuition, there will be no qualified education expenses left to figure the credit ($5,000 - $5,000 = $0). The credit will be zero.
If, however, $4,000 of the grant is applied against the room and board and the remaining $1,000 applied against tuition, there will still be $4,000 of qualified education expenses to figure the credit $(5,000 - $1,000 = $4,000). That $4,000 in qualified expenses could entitle Danielle's parents to the maximum of $2,500 in education credits if all the other requirements are met. Danielle would need to include the $4,000 in income if she is required to file a tax return. If this is her only income, she would not be required to file.
TurboTax will default to applying tax free assistance against education expenses qualifying for the credit. An entry in "Total used" on the "Pay for Room and Board" screen will change this allocation.
