Your question labels this a license but you say you purchased it - and there's a big difference. What does your contract say? You may have a great case is this was a purchase, and you own the software forever no matter how badly it deteriorates and how few machines and other progranms will run it. But if it was a license subject to the discretion of the owner and they could restrict how many machines you could use it on, how many backups you could have, or how many years you could use it, then you have no case. Your rights and remedies, including the jurisdiction and forum you agreed to use to resolve any disputes, depends on what your contract says, and it seems very unlike that the contract provided that you could sue the software owner in Small Claims court.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The software was probably licensed to you. If you try to install it again there will probably be a license click through agreement. That agreement will probably state when they can do this. You'll at least want this before your day in small claims court. Still it does seem rather onerous. I have some software that is multiple versions behind the latest and I'd be pretty upset if the software company killed it. Have you searched online for this happening to other people?
With respect to the other responders, I wil defer.
However, with respect to the age of your software (five years), I wonder whether it will be economically feasible to pursue the issue, even in small claims court. After five years (and several software service pack upgrades) our software (if no longer supported) might not function with the updated version of your operating system software (such as Windows, Linux, Leopard, etc.) It is entirely possible that the defendant software company did not "turn off" or deactivate your software, but the software simply no longer works with your operating system.
Further, with resepect to the agreement you liely aquiesced to, your recovery (even if you can prove that the company deactivated your software, is likely liited to the original software cost. However, the Magistrate (since small claims is really a court of equity) could possibly view the software as having been a consummable commodity (as would be a clear issue in any class-action) and say that you got the value of your purchase; that no software is guaranteed to work forever.
The thing is, no software is guaranteed to work forever. And most software EULA (End User Licansing Agreements) acknowledge this and limit your rights accordingly.
Bottom line is that, unless this software was designed primarily for a business purpose and there is some extensive detrimental reliance based upon some sort of reassurance or promise made by the vendor, your economic loss is likely minimal - in other words, don't spend good money chasing bad.