Tube Amps With Good Bass Qualities

When I had my Legacy Audio Focus 20/20 speakers and drove those with my Rogue Audio M-180 monoblocks, the bass was stupendous.  That didn't stop me from combining them with 4 subwoofers though. 

New, these are over your $5K budget, but I bought a second hand pair here for much less than $5K.

jwlaff

If you’ve still got the Klipsch Heresy’s, anything good sounding will do, as almost rubbing two sticks together will drive them. https://community.klipsch.com/uploads/monthly_02_2016/post-453-0-91780000-1456333330.jpg

If your set on tubes, probably OTL’s would be your best pick.

I had the Heresy’s this is what I would do.
The Schiit 25w Class-A Aegir would be a cracker for just $799 So long as you don't want big party levels. https://www.schiit.com/products/aegir

If you’ve got the bi-ampable Heresy’s
https://cdn.gearpatrol.com/wp-content/uploads/2018/04/Klipsch-Heresy-III-Review-gear-patrol-slide-5-...
You could then go horizontal Bi-Amping with the Schhiit Class-A Aegir on the mids and highs and the $699 Schiit Vidar for the bass. https://www.schiit.com/products/vidar now that would be a killer combo for less than $1500 and you can trial them for 15days.

http://av2day.com/wp-content/uploads/2014/05/biamp1.jpg

Cheers George

Tube amps have excellent bass with easy to drive speakers.Rogue,Prima Luna,Atma Sphere are all good choices.My Aric Audio amp provides all of the powerful and nuanced bass I could ever want.

my 4 watt decware mini torii has decent bass with Ref 3A de Capos

Amps don't make good bass.  Speakers create music, including bass response.

While it's true that different designs and different tubes will sound different, if you need more bass you need to find a speaker, compatible with your amp, that will deliver the bass response you are looking for.  With your music, in your room and with your ears.