Well, I think you should stretch a little and go for the Atmasphere GaN momoblocks or the AGD Tempo di GaN amp as they’re only $400 -$500 over your budget and will very likely give you many years of SOTA sound reproduction. As a backstop and if you can’t stick a crowbar in your wallet and buy one of those amps, an option that’d still give you awesome sound but at a huge discount is a McCormack DNA-125 with full SMcAudio upgrades for $1750 where the upgrades alone probably cost upwards of $2000. This is a near SOTA amp by many accounts, and you can send it to SMcAudio and have them install their Gravity Base Jr. for $400 or full Gravity Base for $900 and up the performance even further and still be WAY below your $5k max.
If you can stretch I’d go with one of the GaN amps, but if $$$ is a concern I highly doubt you’d be unhappy with the upgraded DNA-125. Of course another option would be the $3k LSA GaN amp from Underwood Hifi. It never ends, but I’m sure you’ll be thrilled with any of these awesome amps and your excellent speakers. FWIW, and best of luck.