Instructions for updating ILIAS can be found in section 3 of the general installation instructions. For major updates (e.g. 4.4.x -> 5.0.x) the safest proceeding is, to upgrade a copy of your productive system first and test whether everything works ok.

If you use a customized skin/style, please change the skin settings for root user and default of installation to ‘delos‘ before upgrading from a 4.x version to 5.3.x. Otherwise you may not login any more due to templates changes in former versions.