I have a bunch of bikes, all larger, but the one I love the most is my Ascot. It didn't cost a lot and took very little to bring back to solid running order. It requires very little maintenance. It's a great looking bike, mine has some patina but overall is in nice shape. I'd love to do a full cosmetic restore some day but for now I just keep riding it (reveal: not actually riding it at this time of year). Doesn't have a lot of power but just rails around all day long! Lot's of fun. If I'm going to get into trouble with one of my bikes, the Ascot will be the one. Bonus is, around here anyway, they're pretty rare so there's always somebody that wants to ask questions about it.
Toughest thing about these bikes is finding one with a nice shape exhaust. The originals were 'black chromed' and like all black chromed exhausts of that vintage, they rotted out easily (or the black chrome finish wears off). The finish on mine was a bit rough - it had fallen over a few times. I painted it flat black and it looks OK (personally I hate the look of flat black but it hides the worse shit underneath).
I agree with buying the nicest one you can find but for $5K I think you could get two pretty nice ones. Having said that, I hope I don't come across a really nice one because I'd be very tempted to pay a stupid amount of money for it.