So you have Quark 5, you can create PS files using print, and you can use distiller to create PDFs from these files, is that correct?
If so, maybe check a few of your settings (close any open documents first):
1: Go to Edit > Preferences > Preferences... and look for PDF. In the Acrobat Distiller section, press the 'Select' button and find the Distiller application program. This will make sure that Quark knows where to find it, as it can't create PDFs without it (unless you have Quark 6).
2. In the 'Workflow' section, select 'Distill Immediately'.
3. In the 'Default Settings' section, click the 'Options' button. Go to the 'Output' tab. Under the 'Printer Description' drop down list, pick a suitable postscript printer (whatever one you use in the print dialog box for creating postscript files will do).
Hopefully that should work. If not, please give more details, such as the exact error message you're getting, the name of the printer description you're using, and maybe a list of other printer descriptions available. You should also try out a few other printer descriptions if you don't have any luck.