Yes. It ships with both 32 and 64 bit, and you can use whichever you want at different times. Some plugins don't work for 64 bit so you might need to swap between the two. I think Bridge is only 64 bit in CS6 (and it's very fast!)
Perhaps you are jumping to the wrong conclusions... If he means the original PS 5.0 from the last century and not CS 5 then the answer clearly is no.
Oops! You might be right. I get so used to just using CS
Actually, since pretty much any 32 bit application should still be able to run on a Windows 64 bit system, Photoshop 5.0 may well run. But it may not even install properly on a modern system because of permissions issues, disk size issues, etc. That said, I can run Photoshop 6.0 on my Windows 7 x64 system no problem. I've just not tried 5.0.
There is of course the possibility of running it in Virtual XP.