I've heard a few different phono amps but can't say that I've A/B'd any $5K ones. The best phono amp that I've ever heard (and others who have heard more than I concurred) is the John Atwood designed Artemis Labs. There are two versions the PH and PL 1 - the difference being the addition of transformers for LOMC in the PL 1. The PL-1 lists at about $3K so it's well within your budget.
BTW, the Lector CD player is great. I didn't splurge on that because my main love is vinyl but I thought that the sound was superb.