The upgrade package won't work for upgrading from 1.5.5 to 1.6.2. You'll need to do a new install.
When doing this kind of upgrade, I backed up the complete XAMPP directory first. Then after doing the new install, I selectively copied over files from the old install, and used other old files for reference (php.ini settings, etc.).
Don't forget to backup any MySQL databases you've created, using phpmyadmin or the mysqldump command, so that you can import them into the new install.