Short answer in NO.
To be considered an AP round in Florida, the round has to be larger than .22 calibre, have a truncated cone and be designed for AP purposes. The FiveseveN round that you buy off the shelf does not meet any of these criteria.
I had the same concern and sent a message to the AG of Florida which refused to clarify the question about FiveseveN ammo. They said that it is a question that would be required to be answered by a lawyer and not the AG.
As I can buy FiveseveN rounds in Florida you should not be concerned if you travel here with your FiveseveN or PS90.
I have both, have used them at the range, and have had law enforcement fire both with no problems.
Now if you have SS190 AP ammo, you are screwed. Stick with the SS195/SS197 you are fine.
Now if you already have restricted ammo (SS190/Tracers/AP Designated Ammo) in your posession you are in violation of the law. Does not have to be loaded in your handgun/PS90, just the possession of the AP/Tracer ammo is a voilation.