Tube preamp match with Solid Stare amp

What does “low output impedance” mean?

+1 Backert Labs
+1 Aesthetix Calypso 

Also a Backert Labs fan...currently have a Rhumba Extreme 1.3 and sounds beautiful with either my Pass Labs or Levinson amps.

Audio Research Ref5SE should be a decent pairing. But 10k input impedance is minimum and borderline. I think you may actually be better off upgrading to a very good solid state preamp in your case. 
 

I am using the Rogue Audio RP-7 balanced tube preamp with excellent results; I previously had an RP-1.  I was using it with a Benchmark AHB2 SS power amp which gave excellent results, but switched to a tube power amp (Rogue Stereo 100 Dark), which I believe resulted in a modest "downgrade" in the overall sound quality .... perhaps too much of that good tube stuff.  So, I am going to switch back to SS power amplification, most likely with Odyssey Stratos Extreme ("plus some added upgrades) mono bloc amplifiers.  The RP-7 is excellent, with the low impedance you seek, and at roughly $5K new it fits in your budget. I have had several questions that I directed at the folks at Rogue Audio and received prompt and helpful responses.