The best I’ve used under $1K is, perhaps ironically, the $999 Topping Centaurus, though second to that is the $400 Topping E70 Velvet.
I have no recs for $5K DACs because beyond the $1K mark, the diminishing returns in cost/performance make DACs a rather poor investment in most cases. In my systems, the $400 Topping E70V outperformed an Electrocompaniet ECD-2 ($3500 in 2013), and the $2K Chord Qutest. I believe most listeners with speakers below $20K/pair would be wiser to save the difference toward better speakers.
Recently I heard a tower of expensive Aurender and DCS products fronting some Boulder amps and $80K Rockport speakers. That system sounded phenomenal, but how can I say that had anything to do with the price of the DAC? My hunch is that 90% of the performance was attributable to the speakers and amplification.