I reached by five return limit. I have one more to do and it requires efiling for the NYS return. I can't print and mail it. Do I have to buy a 2nd turbotax software?

You do not have to e-file the last NY return. You only have to e-file a New York return if "your software supports the electronic filing of your return." The software does not support e-filing of a 6th return, so you do not have to e-file it.

Buying another copy of TurboTax will not allow you to exceed the 5 e-file limit.

Is this still valid for 2024?

@johnmun New York prefers e-filed returns, but there are certain circumstances that make it necessary for you to file your NY return by mail and the state DOES allow mailed returns.    If you could not or did not e-file your federal return then your NY return cannot be e-filed.   It has to be mailed.   It is not possible to e-file any state return if the federal return was not e-filed and accepted by the IRS.

https://www.tax.ny.gov/pit/efile/efile_mandate_for_individuals.htm

https://www.tax.ny.gov/pit/file/return_assembly_mail.htm