Do you have Acrobat Distiller? If so, try launching it outside of QuarkXPress to see if there's any problems. You may need to reinstall it.
Quark 5 doesn't create PDFs on its own. It only creates PostScript files and passes these on to a program, such as Distiller, to turn them into PDFs. If you don't have Distiller (or alternative) then you can't create PDFs.
If you DO have Distiller, check your preferences to see if Quark knows where it is.