Welcome to the forum. Please add your location and your bike's model and model year (AFAIK the CX500E was only made for '81 & '82 and both years were the same) to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).
And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bike is about 4 decades old and may or may not have had all of the maintenance necessary to keep it safe & reliable so it is highly recommended to download the Factory Shop Manual for your model (available through the CX Wiki - link in my signature) and go through all of the service procedures, regardless of whether your bike has reached the specified mileage.
I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. You probably know about checking the date codes on your tires and replacing them if they are over 5 years old (yours surely will be) no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip, especially if it is cool or wet). It looks like your bike still has the original rubber brake lines, which should have been replaced every 2 or 3 fluid changes (= 5 or 6 years) so I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid). And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).
As wjvh mentioned, the closest relative to the 500E is the GL500. The engine & drivetrain is the same and the frame is very similar but almost everything else is different.
