After you file

"a tax credit for the full $4000 on my Georgia state return.  "

 

not relevant for purposes of state tax deduction on Schedule A and refund of same.

"why is the full $5000 of the state refund considered "

state refiund is taxable only up to the amount of state tax that was applicable in schedule A, in other words, taken.

For example, if your property tax listed was over $10,000, then none of your state tax was taken.

Review the worksheet for this calculation.