Yes, the taxable portion is what the credit would be based on
HOWEVER
I think you could actually allocate just 5,155 as employee assistance against the 1098-T since part of the 5,250 went for books and if the books are not listed on the 1098-T.
So if the tuition was 9174, which is listed on the 1098-T and the employer gave you 5,250, which 95 went to books (not on the 1098-T) that would leave 5,155 employer assistance you would need to report in the TurboTax program, giving you 4,019 that was added to your taxable income.
If I am following correctly, that would give you 4,019 towards the credit.
Now I see you had those figures in your first post. Yes, I agree.
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