"Good tube Integrated Amps"

PrimaLuna Dialogue Premium HP is right around that price range.  Read the reviews.

Line Magnetic Audio 218ia SET amp. Very nice sound. I have the 216ia and had the 218ia for a short time. It was very sweet sounding.

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.