From the information that you provided, your 1098-T is correct.
Per IRS
Box 1:Enter the total amount of payments received for qualified tuition and related expenses from all sources during the calendar year.
All the amount that was paid in 2021 must be included in box 1 even if it was a tuition for spring of 2022. You made a payment in August 2021 and one in November 2021 so the total $5880 (as you mentioned ) should be reported in box 1.
Box 7: Check this box if any payments received for qualified tuition and related expenses reported for 2021 relate to an academic period that begins in January through March of 2022
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