The ATC SCM19 is a sealed bookshelf design so no ports to worry about and great sounding speakers. Available here with a 30-day return policy and a 10% discount if you submit your email that would put them around $3000 so well below your budget. The SCM20 would be right at the top of your budget if you wanna go bigger. Best of luck.
https://soundapproach.com/atc-scm19-entry-series-6-2-way-passive-bookshelf-speakers-pair.html
My best advice would be to get the speakers the hell outta the cabinet and on proper stands because being in a cabinet is not optimal and will compromise the sound, but if you can’t you can’t I guess.