Yes, if you paid education expenses out of pocket that were not covered by scholarships/grants, you can report those in the Education section.
Indicate you didn't receive a 1098-T and enter your expenses.
It's not clear what you you mean by 'box 5 was checked on 2022 1098-T' as Box 5 is the amount received for Scholarships, so should not affect your 2023 education entries.
Be sure to save documentation for what you paid with your tax file.
Here's more info on How to Claim Education Expenses without a 1098-T.
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