It sounds like the excess (difference between $10,000 and $5250) is a tuition waiver or tuition remission. That is treated as tax free. Tuition waiver/remission is not treated as employer assistance, subject to the $5250 limit. It closed akin to being a scholarship. But, it should not have been included in box 1 of the 1098-T.
Since it was tax free, you cannot claim a tuition credit on any of the tuition paid.
