Finally ! after almost a year since the last update from 5 to 6.
Difficulties were the conversion of the old image nodes to the new nodes + image field flavour. Not everything works yet, enough for me to do !
Time flies ! I just noticed that this site is already running on Drupal for 10 years. My user-id on drupal.org is 4945 ... I'm not so active anymore on the Drupal site, but I guess I'm one of the oldie goldies.
I had to delete a lot of content: all the weblinks (most of them pointed to nowhere anyway), photo's of old friends and some other stuff.
Update: I just found out that the very first version of Drupal I installed was version 4.3.1 → that's a version you can't even download from the drupal.org website anymore (starts with 4.3.2 from March 2005).