I had now an opportunity to try a totally new Ubuntu 16.04 installation, as recommended, using the following installer:
Ubuntu-Mate 16.04 Net Installer
Everything went well, until the the installer tried to finish the installation... There was a red screen and a warning that it was not able to finish the installation, and the problematic phase was something like "finish the installation without loading initial bootloader" (I was not using english in installation). There was also possible to choose "install Grub" but it did not help either. The only way out was to was the last item in the installation menu, 'cancel installation' or like.
When I tested the created new Ubuntu partition, it was able to boot normally (and had already 16.04.5 upgrade), but there was only the 'Guest' account available, which cannot save any changes made! The account I created at the beginning for my own name was not available (or at least did not accept the password), and I was not able to create a new account either (the password I had defined did not work as 'root').
So... How to fix this problem??? I thought this installer was tested and proven to work with X5000....?!