Do I qualify for a repayment credit after I paid off over $5000 in state taxes due in 2024?

I HAD TO PAY BACK TAX OWED 

The money you paid to the IRS for a previous year’s federal tax return is not deductible, so you do not enter it anywhere on your 2024 return.  If you paid taxes due in 2024 to your state or local government, you can enter that by going to Federal> Deductions and Credits> Estimates and Other Taxes Paid> Other Income Taxes.  You can enter the taxes you paid, but do not include any penalties or interest.

A repayment credit is when you were paid money from somewhere and had to pay it back. If you were just paying the taxes you owe, that would be part of your itemized deductions on Sch A and entered as tax paid.