I know this has been posted before (for 5R1 anyway) but this appears to be a new and different problem.
I followed the instructions for installing the latest Adobe Flash 11.2 64 bit listed elsewhere in the Forums and FAQs. I also tried using nspluginwrapper with earlier versions of Flash. No plugins are ever recognized by Firefox.
Also Firefox 14 included in 5R3 seems to have a wide range of issues. For one I cannot log into this (or many other) forums, even with NoScript turned off. No plugin installs of any kind, besides Flash, seem to be compatible with FF14, e.g. no Java, Acrobat, etc either.
One weird bug: I tried a wide range of Flash alternatives. None were overtly recognized by Firefox but I did, at one point, get a Flash video to play, even after Firefox said "additional plugins are needed". I have been unable to duplicate this behavior, however.
FF14 seemed to have other issues as well. I had upgraded in my old BT5R2 x32 install and it seemed to use 100% of the CPU after a while. That, and the recent release of 5R3, were significant motivations to upgrade to x64.
If there are no ideas that work I may try downgrading Firefox, which I hate to do... Incidentally I'm using Chrome to post this. Flash and other plugins also work in Chrome, but it is not as desirable for pentesting, as I'm sure everyone knows.