If automatic upgrades of plugins or your whole WordPress installation do not work, you might need to enforce PHP 5 usage. This is fortunately very simple. In the root directory of your WordPress installation, look for a file called .htaccess. If it does not exist, create it with the following content:
AddType x-mapp-php5 .php AddHandler x-mapp-php5 .php
If the file already exists, just append the above two lines at the end.
Thanks to Schnurpsel for this hint.