It's been a long time but if I remember it right, the CX-7 was their "affordable" CD player of that era. I think it sold in the $3-4K range. The C-5 was a universal player if you remember those. That means it played CD and also DVD Audio and Super Audio CD, and sold for roughly double the CX-7 price. I never heard them back to back, and recall different opinions as far as how much better the more expensive model was. But the 5 should be at least somewhat better than the 7, and it plays more formats if that still matters to you.
I think it went C-5, then C-5xe (with the E standing for Evolution, mostly power supply upgrades), and then C-5xeMP where the MP was for Minimum Phase, a new filter they added.
It's hazy but I don't think they labelled them with a sticker on back saying what the model was. You could send your older player in for an upgrade so even if it started as one thing, it could end up as another, and there's no way to really tell just by looking. But maybe I'm remembering it wrong.
Those were great players back in their day but I think even the newest examples have to be over a decade old by now, or even 15 or 20 years in some cases. I'd be worried about things wearing out, such as the drive mechanism, laser, or capacitors in general. You can email Ayre and see if they have any advise but I personally would pass, you can find some great newer stuff for a good price these days and have many years of life left in them.