Looking for an integrated amp around 4000 to 5000.

 "those Prima Luna tube amps have an output impedance of several ohms! Hardly good for bass performance! My Dynaco ST70 is far better!

White paper vs anectdotal experience often contradict  what anyone's ears actually like.

Having used the PL HP for 5 years, I've never heard a bass deficiency.
Like all amps-ss or tube, some speakers sound good, some don't with said amp. 

The PL HP has both of the OP's requirements and plenty of flexibility to tailor the sound(tubes) to the OP's liking. It will also drive many popular speakers. Whether  your ears like it, that's all YOU and no one here.

You simply need to demo if possible. All the write ups on it, do provide insight, but no guarantee for your own ears. Reselling if you didn't like it, shouldn't be a problem.

Check out Line Magnetic as another value tube option.

Thanks everyone for all of the advice. I will look into your suggestions. 

I think the ML 585 has a DAC. Build quality is great. Luxman 505ux is a good sounding integrated. I used that with Harbeth SHL5s and great synergy. Pass makes some nice integrated sound as well. Always best to audition in your home if possible! 

@Pal, what is the Rogue not doing in your system? Have you rolled 12AU7s to better serve your wants?

You can pick up a used Naim Supernait 2 for relatively cheap now that the SN3 has just been released, but even a new SN3 would fit in your budget.  Won't have balanced input, but it'll do you right in engaging you with the music, is built like a tank, and drive most speakers you are liable to throw at it (should be fine at 88db sensitivity with yours).