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Version 5 is not compatible out of the box, but it is if you use the Launcher. Try googling for Parallels 5 Launcher or similar:...
It turns out there actually is a way to use Parallels 5 on Lion, though networking seems to not work. Google for "Parallels 5 Launcher" or...
Not sure why it worked fine at first, but Parallels doesn't want Version 5 to run. You not having saved the downloaded file is on you - maybe you...