Older versions of Flash used to specify 44.1 kHz and I forget what bit depth - you might check your mp3 settings and see if CS5 documentation has suggested bitrates and depth that are supported.
I think there could be a problem with the mp3 files that you are trying to import to your flash player.
If you have adobe media encoder, you could try to play the mp3 file using that software. If it plays fine then you must be able to play the mp3 without any issues.
Secondly Flash does not support 64 bit operations. Since you are using a 64 bit machine, it could have some relevance to that.