Looking for an integrated amp around 4000 to 5000.

Hegel H390.  I have a Hegel H360 and it is outstanding.  I hear that the H390 is even better (have not demoed).  Retails for $6000 but you can get it brand new for under $5000.  I have not heard a better amp under $10K.  Musical, and grips the music, particularly the bass.  Plus all kinds of connectivity, including a top-flight DAC.  Not sure if it is Roon-ready, but it's supposed to be by now.  250W X 2 @8ohms with a damping factor of more than 4000.

Second or third what Chorus recommended.

The Hegel H360 or H390 is superb - excellent dynamics, prat, resolution and clarity, as well as bass control.

You might also consider the McIntosh MA252 / MA352 (tube hybrid).

Can't go wrong with primaluna. I love my prologue bought used. Best sound ever.

Belles Virtuoso, when it becomes available.

The newly introduced NAD M-33 is worth a long look. It checks all your requirements and adds a few. MSRP is exactly $5000. Check it out. It looks to me at age 73 like a geezer's dream come true.
I'm currently using the M-10, which is a great unit in its own right. M-33 is more and better all the way around. Bluesound is very good and very convenient.