Looking for an integrated amp around 4000 to 5000.

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. 

PrimaLuna HP (14 tubes!) with my Vienna Acoustics produce excellent, tight bass. Luxman solid state was unexciting in comparison. Rotel and Parasound were okay, but did not equal PL.