So it seems that you may have an '83 CX650C with an '82 CX500 engine.
Here's the odd thing: The engine number says CX500E but the 500E came with the more squared off valve covers like the 650 engines have and yet you have the X500 models and the GL500.
But that could be something as simple as a Previous Owner thinking they look better (as I do).
I think the important thing to know will be whether the engine is set up for Transistor amplifier Ignition (TI) or Capacitor Discharge Ignition (CDI). I expect it will be TI since both the bike and engine came with TI but you never know so it is worth verifying.
Want to know whether your Honda CX or GL has a CDI or TI system, or looking for more information about each setup? Find out here!
motofaction.org
I'd bet this trike has an interesting history....
BTW: We love to see pics of everything so please post more