Since you have several questions, allow me to split them up a bit. Keep in mind that I'll be answering these questions as if you were a US customer since that's the info I have:
Is there a player that I can purchase that supports this speaker system? (If so, which one?)
The speaker systems are not interchangeable from year to year and generally not from model to model. Besides this, when you buy a Samsung receiver by itself: it uses standardized connections for the speakers, but when you use a Samsung home theater, the connections are proprietary.
Can I purchase a speakerless home entertainment system?
Yes, you can purchase a receiver separately, but it won't work with your existing speakers.
Or could I just plug the speakers into the TV?
No, you can't plug them into the TV since the speakers cables have proprietary connectors.
I've recently bought a Samsung UE60ES6300 online (it's in the process of being sent) which will replace a smaller Samsung TV that is hooked up to a Samsung HT-C5550 home entertainment system.
Now the new TV supports 3D discs, but the HT-C5550 system doesn't. So I need a new player. What I don't want to do is buy new speakers (it's a 5.1 system). Is there a player that I can purchase that supports this speaker system? If so, which one? Can I purchase a speakerless home entertainment system? Or could I just plug the speakers into the TV? Thanks in advance.