Mr Alomds, I suspect the $5 Sony DVD/CD player is something like a s725, or similar. The DAC section in almost all those older Sony DVD Players was based on the Burr/Brown chip set. Short of an external DAC, it's about as good as it gets for a built-in. I think you should pat yourself on the back and enjoy the sounds.
Of course you can take the optical out to an external DAC and feed that into your system. But for casual listening, there is nothing wrong with that Sony DVDp. I have used many of them over the years for second systems. They work well. The only drawback is when playing a CDRW with MP3's, they are bit slow to jump ahead when skipping tracks. The remotes all seem a bit laggy doing MP3's.
Why would I play MP3's - well the cool thing is that you can write about 80 tunes, or more, to a disc (my rips are all at 320K). That means all of your Christmas music can play in the background while you're are having egg nog with friends, etc. Ditto country & western for the 4th of July, etc.
Of course you can do that streaming too. But that ties up a piece of computer equipment, or your phone. And those can be interrupted ...