Best Integrated that you've heard under $5k

Focusing only on the amp or prioritizing the amp without regard to the rest of the system, as if the amplifier is the key to a good system, is a beginners mistake. 

Linn always advised one to focus on the source:  get the best source you can: put the bulk of your time and money into your source. The recording quality comes first in this. A poorly recorded LP, or dirty [well recorded] LP is going to sound bad no matter what the system. In fact the better the system the more you will be hearing the flaws upstream. The LP or CD player or system and its synergy comes second.  A bad turntable support is going to 'make bad' a great turntable [support isnt an issue with CD gear]. The preamplifier quality is next in the 'Linn' hierachy. Next is matching the amp and speakers. Great speakers cant make a bad amp sound good.  Oh well.

I use a Belles Aria Signature and it lists for $4500 but I did not pay that...;-)

Muscular yet with finesse and it's a keeper.
Driving Dyn S-40's and soon Heritage Specials.

Line Magnetic 805IA, Leben CS600, both very special

Hegel H390 in my experience.  I preferred it to McIntosh MA352 (overly saturated and flat soundstage) and LTA Z10 (a bit thin sounding but amazingly transparent). I would put it up there with Pass XA25 and First Watt SIT-3 power amps I had before (using digital volume control, so no preamp influence there). Not quite as sweet and dense as the Pass stuff, but a little more detail, significantly more bass authority and cleanliness, bigger soundstage. Overall the Hegel is a better all rounder with a lot more features.  I got mine new for a good chunk under $5k.

I haven't heard the Coda CSiB but was looking hard at it before I went whole hog and replaced the Hegel with something much more pricey.

Aesthetix Mimas,
LFD mk. IV.