You should be able to get some excellent sounding speakers for that budget - especially if you buy used, and you’ve gotten a lot of great advice here so far. It doesn’t sound like you have been doing a lot of listening to different speakers and systems recently. I heartily recommend you go to Chicago and listen to as much modern gear in person as possible. Or take a trip to someplace like The Music Room in Colorado where they have a bunch of high quality used speakers in your price range advertised here on Audiogon. The investment in time and travel cost will be paid back in spades in raised awareness.
While I agree that it is difficult to guess how a speaker that sounds great in the showroom is going to sound in your room with your gear, there is a lot to be gained listening to different gear combinations to see what they do well and what they lack. I listened to all kinds of gear at all price levels in showrooms around the country to understand things like amp and speaker matching and came to understand that for me, tone, timbre and dynamics were more important than soundstage and spatial resolution. That experience ultimately drove my buying decisions because I was able to focus on those characteristics when demoing the amp and speakers that I ultimately bought.
Different elements of sound reproduction may be important to you, but building your personal listening vocabulary is critical to getting what you like on your budget, and even to more effectively demoing gear in your own space. Imagine doing research ahead of buying some expensive visual art without ever looking at any pictures or visiting any galleries to see the pieces in person, but just basing your buying decisions on critics reviews and the opinions of other art collectors. I hope you get my point.
All that said, some of the speaker suggestions already made here seem potentially well suited for your musical tastes and can provide a bit of narrowing for your search. ProAc, Vandersteen, Dynaudio, Monitor Audio, ATC, Totem and Revel all have potential to reward. I would add Spendor and PMC to that list. At $5,000 speaker budget, I might suggest a very nice stand mount in combination with one or two subwoofers. For a warm and woody sonic hug, check out a pair of Wharfedale Super Lintons and an REL Classic 99 sub. Or, you can go all in on an active tower like a used pair of ATC - SCM40a Active Floor-Standing Speakers, or something like a Dynaudio Focus active stand-mount plus two REL S/510 subs. With active speakers you can do without a new amp entirely and put your whole $6-10k budget into powered speakers (and subs), and just drive them all with your preamp.
No matter what, I really suggest you get out and listen to some of the newer gear with your own ears. I think you will be blown away with how good hifi has become in the last 25 years at lower price points - especially with respect to bass reproduction and dynamics.
kn