A CX500 can pull 80k miles or well over. Tough, tough motor.

If you get it: check and change the plugs, put good synthetic motorcycle oil in it with a new filter, check and adjust the valve clearances and cam chain tension. Change the radiator fluid. Make sure the stock-type air cleaner is OK, change if it looks wonky at all.

Next, take the seat and tank off and with winch straps lift the front end up in the air, with the forks and handlebar free-swinging. Yes, really. Rear tire can still be down or put it on the centerstand if it still has one - you only need the front tire an inch off the ground. Winch straps are cheap at any hardware store :). Grab the lower fork tubes and make sure there's no extra play at the steering head. Looseness or slop there can kill you. Worst case you may need new bearings - it's not that hard to do.

Now use the centerstand or winch straps to get the rear tire off the ground. Disconnect the rear shocks at one end each - lower is better but either will do. You need to check the swingarm bearings for slop for exactly the same reason you checked the swingarm bearings. OK?

Next...with seat and tank still off, look at all the wiring. You're looking for worn spots, corroded connectors, anything shitty of that nature. It'll probably be OK.

Using a voltmeter make sure it's putting out 14v or more DC while running. A repair manual will tell you where to check to make sure the charging system is good.

A failure at the battery or starter should NOT leave you stranded because if it's running good and the charging system is OK, you'll be able to bump it. I would try bumping it as a test, flat ground, pushing it and starting in 2nd gear. If you can do that, cool, it means you have a "plan b" if the battery or starter fails.

With the above checked and decent tires, I would take an old CX500 cross country in a heartbeat.

Flat-tracker type handlebars are a "to taste" thing but in my opinion they're much better than the stock "buckhorns" on that thing.