Within your $5K budget, I'd recommend the Vienna Acoustics Beethoven Baby Grands with a REL sub woofer. You only mentioned tight/powerful/fast. If you go with the setup I'm suggesting, you'll get that plus you'll hear the true character of the bass. With double bass you'll hear the woodyness of the body, with electric bass you'll be able to tell a Sadowsky from a Fender, etc. Lot's of systems get the TPF right but leave out the character. For your classical listening you'll really need that.
Hooking up with the Sumiko guys (distributors for VA, REL, OCOS, Sonus Faber, Pro-ject, Sumiko, etc.) will get you in with some guys that really know how to put a system together.
Dave