I bought a used McIntosh MAC6700 well under that and it has everything I need. You might even be able to get the HD Radio TM-3 Tuner for it and still be under $5000 too. I am still amazed by how clear HD radio can sound through my system, and I never even listened to the radio at home until I had it.
Also, I heard the latest Anthem STR at Axpona in 2019 running into a pair of Paradign Persona 3 speakers. They had it set up in a hotel room (as is most of the show), and I thought they had the absolute best sounding hotel room in the whole place. I don't think you could go wrong and I think you could get that new under your budget number, and probably even less if you could find one used.
Good luck!
Also, I heard the latest Anthem STR at Axpona in 2019 running into a pair of Paradign Persona 3 speakers. They had it set up in a hotel room (as is most of the show), and I thought they had the absolute best sounding hotel room in the whole place. I don't think you could go wrong and I think you could get that new under your budget number, and probably even less if you could find one used.
Good luck!