not sure I follow how you are using the terminology - the tax credit for solar can't reduce Line 22 below zero... please look at your Form 1040.
so if your TAX (line 16) is $5000, then the solar credit for 2021 can't exceed $5000 (line 20) because Line 22 can't go below zero.
if your tax credit for solar is $15,000 and you just used $5000, the rest will defer to see if can be used for 2022
when you state you "paid in $10,000" - what does that mean? you made estimated payments against your tax due?
