Tube Amps With Good Bass Qualities

Look at Linear Tube Audio. Bass like solid state.

I owned a Prima Luna 40 wpc integrated for a short period and thought the bass output was outstanding.

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.