Time For a CD Player Upgrade

@wspohn 

I've done that and compared, and there is certainly some degree of loss or error that happens when moving the data from CD to computer. The CD's still sound best. Same DAC, high end computer, etc. I personally went backwards from high-end computer/hard-wired directly to DAC to using CD's on a McIntosh MCT500. 

The most natural sounding CD player I have heard is the Ayre CX-8.  A bit above your stated budget new, but someone with audiophilia nervosa may put one on the used market…

I’ve been using a McIntosh MVP-871 CD/SACD/DVD player that’s about 14 years old and has a built in DAC.  Fortunately, it has digital outputs for sound so I connected it via a glass optical cable to my new MX-123 which has an modern internal DAC. Without question, sound quality was significantly improved. So, if your player has digital out capability, I’d try connecting either through an external DAC or connecting to your preamp digitally if it has a decent built in DAC. You might find it unnecessary to replace the player!

upstateaudiophile

... there is certainly some degree of loss or error that happens when moving the data from CD to computer.

Something is wrong with your setup if that’s true. You should be able to get bit perfect copies of any CD, with the exception of those that have been damaged. You can verify that for yourself by running a binary comparison, such as using the "fc" command in Windows.

Often, you can get pretty clean copies even from a damaged CD.

Easy, as said multiple times, transport and dac. Lots of options for 5k. Google search is your friend.