Ubuntu ruing slow

Hi Christian and welcome to the forums.

An "older version" is never a good idea. Anything that is still supported won't be appreciably faster. On the other hand, anything old enough to be reasonably fast will be so far past end of life as to be a security disaster waiting to happen.

In the 'buntu world, reducing overhead and increasing speed is addressed through selection of the 'buntu flavour (desktop GUI) and not the version (age). v3.xx is correct. Mate or Lubuntu will go much further in giving you a decent experience than regressing to some dangerous out-of-support version.

The DC5800 is not really that ancient and should run a low-graphical desktop just fine. Its bottleneck is not the CPU but the GPU and, to a lesser extent, RAM. Increasing RAM always helps, but in your case, the GPU will be the biggest limitation. It is one of those early on-board chips that steals its DRAM from system RAM, which limits the amount of system memory even further. It's usually not worth adding a standalone graphics card to such machines. You are better off adding memory and ruing a lean 'buntu flavour like Mate or Lubuntu.

...and stick to 14.04 and soon, 16.04. Stay with Long Term Releases.