A tube pre-amp would offer a different sound, for sure, and you’d have to decide if it would be a big plus. A budget going up to $5k for just the pre-amp opens the floodgates for many, many options, plus tube substitutions which can also vary the sound.
Not sure from your post if you're asking about just a pre-amp or a pre-amp AND an amp. $5k would be sufficient for both, but you could really get an amazing pre-amp with $5k as your available budget. You could also get a pre-amp first and then add an amp later.
Rather than suggest specific models, I can tell you what parameters might be worth looking into:
-- matching impedance between preamp and amp: PS Audio has a post on it and you could also email them or search the forums here. See, e.g.
https://www.psaudio.com/pauls-posts/mix-and-match-impedance/-- seeking input from Heresey owners about what they’ve liked.
Good tube providers are also very important to know about -- I’ve had good experiences with Brent Jessee, Jim McShane, and Vivatubes.
I’m sure many others will pile in on this thread with better information, but hopefully this helps get you thinking about some general directions your inquiry might advance.