The reason this is happening is that in PAF 5 the slashes are used to mark the SURNAME (regardless where it appears in the full name). See Tools menu > Preferences > Names. So the list is alphabetized by the name marked as the surname.
The problem is that the wrong name is marked as the surname. Check the copy of your database on your old computer to see whether the slashes are in the right places. (If you used PAF 4 in the old computer and the names are correctly identified, try exporting everything to a gedcom and then in PAF 5 create a new file with a new name and import it.)
Failing this, you may have to edit each name to put the slashes around the surname. I have tried a variety of other approaches but nothing worked.