"Good tube Integrated Amps"

Hi there
for 5k you can get a used audio note meishu (the sweet spot in the audio note UK lineup). It is a very highly regarded integrated amp. I've had mine for 20 years and i get everything i want out if it in a 350 square foot room and 93db speakers. You will need fairly efficient speakers unless the room is small. 

pear audio blue Classic intergrated at 4K ,

A must listen is the Audio Research VSi60 or VSi75.
They punch well above their weight, and have the solid ARC house sound.
I might be selling mine (VSi60) in the coming weeks, but it would only be to go to Audio Research separates. But I’m gonna let it take a swing at pushing my Wilson Audio Sashas (in bound) when the arrive.

How much power do you need.   Eastern Electric makes very nice products for the money.  They are built like tanks and some have many features  for tweaking the sound like my M520 25w/ch but can drive small Maggie's in a small room no problem .   Bill at Morningstar audio is excellent to deal with. 

PM me if you decide to sell your VSI60.  I had one a few years back and really regret getting rid of it......