Hello Lausvi,
The Beocord VX5000 is a difficult machine to work on, due to it's extensive feature set and the age of the electronics inside it. It is the only model in the VX range which contains a digital frame store circuit, and this contributes to the heat produced by the unit in operation. Almost certainly the problems with your second VCR are caused by bad electrolytic capacitors which have failed due to age and heat. The problem is that there are around 150 electros in a VX5000, so any repair is going to be very time consuming, and unless all the capacitors are done at once any repair will be short lived.
You should also be aware that the video head drum has been discontinued for this model, so if you intend to use the VCR on regular basis, you should replace it with a more modern unit.
The circuit boards are not easily separated to work on as they are wired together with a short set of interconnections which do not unplug, so you have to balance all the boards in a very awkward position to gain access to the under side.
The other well known fault with this model is the capacitors on the capstan motor can leak and destroy the capstan motor circuit board, (which is another discontinued part).
I'd advise trying to pick up a late production VX7000 or VX8000 to replace what you have, as they are pretty cheap since most people are switching over to DVD recorders and hard disk recorders these days. The later model VCRs don't run anywhere near as hot as the VX5000, don't have the same temperature related problems, and use a different capstan motor which does not fail in the same fashion.
You may still opt for repair, but I thought you should be aware of this information before you proceed.