My last Integrated Amp: $5-10,000?

I had an Audio Research GSi75 a couple years ago.  It was phenomenal with a superb DAC and phonostage.  My large space and fairly inefficient Wilson Sophias simply needed more so I went back to separates.  I then later dabbled again with the ML 5805 and 585.5.  The 5805 impressed me a LOT!  It was definitely stronger than the GSi75 and my Sophias were very happy.  I knew that I would not be happy having a mid-line model so returned the B-stock item to Crutchfield and found a demo 585.5 from a dealer.  A few weeks had passes but when I first listened I was disappointed.  It didn't impress the way the 5805 did and there is no logical explanation for that.  It also had a bad capacitor and was picking up a Spanish AM station.  Nothing wrong with a little festive Spanish music but that wasn't going to work either.  I did not want to have a newly purchased item serviced so thankfully the dealer took it back.  Hope that little bit of experience helps and good luck in the search.

I agreed with @ghdprentice , besides the price, these different amplifier sound very differently.which sound you like? we do not know and you do not know.you can't purchase with blind eye. You got come to the dealer and demo listen your favorite music, longer than one hour for each brand  and you decide.

No one mentioned Jeff Rowland class-D Continuum S2?

 I love mine very much

Many terrific suggestions here, the only (obvious) thing I’ll add is your choice of amp will narrow the selection of speakers that are best suited to your system and tastes, so it’s good to factor what your starting point speaker will be. I don’t think there’s a right approach to building your system around the amp vs speaker but speakers are far more variable so I tend to build around the speaker once I find one I like. And FWIW my amps have changed at about 5x the frequency of my speakers - I had my first set (Merlin TSM) for nearly 20 years, though with a few upgrades along the way, went through an experimentation phase with 2 transitional speakers (but honestly the real factor was I had more means), and I don’t intend to change my current ones probably for the next 10 years. Amps are also far easier to trade on the used market than speakers which makes swapping more straightforward.

(Also FWIW, my first choice integrated for my next system is the Gryphon Diablo 120 but that is also because it works exceptionally well with my favored speakers.)