Does reinstalling TT on the same PC count toward the 5 license limit?

I know I can install TurboTax on up to 5 computers based on the license terms. This year I had to reformat my SSD and perform a fresh install of Windows OS on my laptop twice - and TurboTax 2023 as well.  I want to reinstall TT2023 once again - so this will be the 3rd install on the exact same system.

  1. Does each install on the SAME computer count against the 5 limitation? Meaning after this I will have two left?   or
  2. Does the Intuit server recognize some identifier specific to my laptop, knows that this is a reinstall on the SAME laptop, hence I have only used 1 or of 5 allowed licenses? (edited to cross out a typo and made the correction)

Thank you