A common problem with the CX500 is with it's timing / cam chain tensioner. The '78 models had a recall on this part, due to the guide bolt backing itself out.

"THE CAM CHAIN GUIDE BOLT MAY LOOSEN DUE TO THE PRESENCE OF A RUBBER COATING ON THE SURFACE OF THE GUIDE IN THE AREA WHERE THE BOLT SEATS. IF THE BOLT BECOMES LOOSE, THE ENGINE WILL DEVELOP A TICKING NOISE. CONTINUED VEHICLE OPERATION WITH A LOOSE GUIDE BOLT MAY RESULT IN BREAKAGE OF THE BOLT AND INCREASED ENGINE NOISE."

Recall details here.

If your '78 model had the recall remedied by a dealer, you will see 3 punch dots on the engine casing in this location:

If your bike is a '78 and does not have these punch marks, you need to update the tensioner.

The manual requires that you check the timing chain at 20k miles. Doing so is usually an engine out operation and is referred to as the Triple Bypass. Triple because there are 3 elements to the CX engine that are common failures and all are engine out operations - thus, doing all three at once is preferred preventative maintenance. Them being the water pump mechanical seal, stator, and timing chain / tensioner.

Here are some invaluable links for CX owners:

Triple Bypass Parts List

Links to all common CX issues.

My CX has 26k miles on it, and has had the recall addressed. At the end of last season I suddenly got a metal slappidy noise coming from the engine. I rode it 2 blocks to the apartment and then had it towed from there. 2 blocks can do a lot more damage then I imagined.

What happens is the chain is either stretched beyond spec, or the tensioner lets go. In either case, this causes the now loose chain to run against an interior plate that blocks off the crankcase. 2 blocks of riding, at around 3k RPMs means about 3,000-6,000 revolutions of that chain grinding away at your casing.

Here's the aftermath of what it did to mine:

You can see it ground off most of the screw boss, screw head, and the lower casting protrusion.

Upper screw boss wear.

Broken right chain guide.

Broken left chain guide.

The semi-good news is the crankshaft bearing plate that the chain ate up is replaceable and not to expensive to pick up used. They pop up on eBay for around $20-50.

1978 CX500 microfiche

The amount of life your chain has left can be checked without removing the engine.

Here's how.

Using the dental mirror method, you're looking for the amount of travel the cam chain guide bolt (#15 above) has left to move in the channel of the guide plate (#5).

Here's a diagram explaining what you're looking for: