The VX5000/5500 has very serious problems with the caps. More or less ALL of them must be replaced, sorry, that's a lot of work.
This here is the real amount of bad caps of ONE VX5000. They are all bad after 20 years.
Especially the 3.3uf caps are the worst s..t ever used in a B&O.
And one of them is your problem...
OK, first try... on the upper mainboard is the video switch section, grid B2 B3, there are a lot of 3.3uF caps, 2x100uf and 1x470uf next to the foil cable. Replace all these caps first, use 105 degree types and miniature types. They have one big advantage: they are easier to replace and then there is more cooling air around these parts... it does not become so hot any more. Usually this is the section if you have a black picture.
But... be sure it wont last very long, then the next cap fails. I have tried several times, just tu repair the real defect parts of them, but it's impossible. Even after some minutes or hours testing the next one fails. I recommend to replace ALL caps. Replacing only some of them will fail sooner or later.
Begin with the power supply and the 12V regulator unit, capstan upper mainboard, lower mainboard.
Have you checked the lithium cell? If this cell fails, you have usually this defect that it does not startup correctly.
Martin
http://forum.beoworld.org/forums/thread/76448.aspx