We have successfully upgraded a Drupal-5 website to Drupal-6. Just follow the UPGRADE.txt file that comes with the package, with one minor point as below:

Just before you are about to move away the old Drupal-5 directory, goto the page for module uninstall page at admin/build/modules/uninstall. Check if you have any modules that are no longer needed after the upgrade. If you do, uninstall it first. If you know you won't need a custom module anymore, but don't see it listed in the "uninstall" page, check the module.install file. You may have to add a function module_uninstall(), and add the code for dropping the tables created by this module.