It counts by Intuit user id. In short register another user/email id with TurboTax account and install it on another computer if you have one. If you install on same computer it will not ask for new license key you will be blocked again.
I had similar issue where after filing my 2nd return TurboTax incorrectly started to show that I had filed more than 5 returns. After staying on the call with TurboTax support and uninstalling old copy and reinstalling a new copy on same computer I was blocked again to e-file again. New licensed copy never asked me to enter the license key. There is no option in software to change to new key. At that time TurboTax support agent disconnected my call and never called back. I guess he was out of option but I tried on another computer and I was able to e-file.
