Integrated amp under $5k

Peachtree Carina X or Carina GaN

Integrated class D, check out the Heaven 11 Billie. 
 

Class D power amp, check out the Orchard Audio Starkrimson Ultra. 

The Axxess Forté series of integrateds are the best implementation of Class D I have encountered, both integrateds and separates. I suspect that’s because their distortion profile is 2nd order dominant, with all higher orders being inaudible. They are rated at 100 WpC, but actual output is approximately 170 watts into 8 ohms and 250 watts into 4. The onboard DACs are stellar too. 

HIfi Rosę RA280 is worth a look.

I really like my new Atoll IN200 evo I got from Paul at:

https://minnesota.audio/collections/atoll-electronique/products/atoll-electronique-in200-signature-integrated-amplifier

Dual mono design, incredible grip and bass on my ProAc studio 148 slim towers, very mids and highs also.  I got the optional DA100 DAC board that also sounds great.  Very clean design with 120w 8ohms / 200w 4ohms, a clean remote plus one of the very, very few integrated amps that have a switchable tape loop.  It bettered my Audio Refinement separates (for sale, designed by YBA).

I would stay away from previous versions of the IN200 (non-evo models) as they were not as well as reviewed given the IN200 evo was made to very close specs and techniques used in the very well reviewed IN300 by A British Audiophile here:

https://www.youtube.com/watch?v=VQzAReJFbDU