The bike misses when going 55mph

1 Main Jet clogged, 2 not correctly carb sync, 3 bad air filter, and I hope NOT - bad engine compression.

No this model did not come with a fuel pump. Actually the VT 700 Series was the only Honda from 1986 that contained a fuel pump.

try draining the tank and adding new fuel,depending on how long its been sitting not good for the engin

The fuel filter is in the tank on the petcock and is self cleaning. I suspect you have bad spark plug caps on your bike the cap is part of the wire. If you remove the wire and take a reading with an ohm meter, the cap should read 5000 ohms . Anything above or below and you should replace the cap. This is probably causing the slight miss.

Carb or air filter need looking at .Fule or air problem

best thing to do is reset mixture screws to standard then get the carbs balanced,it will make a big difference

try e-bay first. if you can't find it there google piston rings for your honda shadow vt500c.