I looked into these when I picked up a set piled in a box at a yard sale. I think it was an Ampro brand or something like that. The little selector lever had apparently fallen off and I had to make a new one after finding that theirs is a 'receipt-only' warranty (I mention this only as a heads-up for anyone contemplating this brand tool). It was missing two metric sockets and thought it would be easy to find replacements. Wrong. There's all different schemes to fix the socket into the ratchet.
This variety of different drive configurations is why I think it's so difficult to find individual replacement sockets. They're made and sold in sets, and I imagine the demand for individual sockets having whatever unique drive for that particular set that the brand was selling at that particular time would be so small that establishing another thread in the distribution chain for them is simply not worth it. No reason to tie up valuable retail space on with them, and shipping for a single socket ordered online would probably far exceed the cost of the socket in most cases. Let alone trying to determine what year's production your socket is.
Closest I saw to a 'standard' was a 3/4" hex stud on the sockets. Every pass-thru set I saw having a plain-old hex stud on the socket was 3/4" drive. But even with these, some kinds have the friction ball in the ratchet while others in the socket hex.
HF had the best socket match. I read the reviews and everyone said the ratchet was pure trash. Here too, sets only, no individual sockets, and only a few locations actually carry them in-store. Wasn't going to spend $20+ on a set just for the two sockets. The HF is a 3/4" drive, not a 5/8". At least what they were selling last year was a 3/4.
I never found a 5/8 size drive in my travels. If CM no longer sells that size, you'd be best off buying a complete new set. Wouldn't worry about the drive style, hex, spline, etc. You're not likely to find replacement individual sockets for any of them, and next year your brand's drive may differ. Just buy everything you think you'll need at once, and from a brand you know has a good warranty.
