How loud can I listen to my P3esr without damage?

I sometimes listen to jazz with my P3esr at about 85dB average (at 1.8m.), reading from iphone app. Would like to know if it's safe for my Harbeth. My amp is Luxman 509X rated at 125W at 8 ohms and room is 4x5 m if relevant.
Without damage to what? The speakers? Or your ears??
As long as you don't drive the amp into clipping there should be no problem.
Without damage to what? The speakers? Or your ears??

to my harbeth.
They should be fine.  Out of curiosity, I got out my SPL meter and played mine at that level at about the same distance, using my Vincent SV 237 integrated, which is 150 WPC.  That's a little louder than I listen, but is more likely to damage your ears than the speakers.
I would be more concerned about long term permanent hearing loss 😎
Power handling per the manufacturer is 50 watts. With a speaker sensitivity of 83db, 90db peaks at 1.8 meters would require 16.2 watts. 95db peaks would require 51.4 watts. 95db is very likely the SPL limit of your speakers before damage becomes likely. Sustained power handling is usually about 2/3 of max power, so in this case it’d be ~25 watts.

Since most phone apps measure between 5 and 10db lower than a real c-weighted meter, you’re likely listening at higher SPLs than you thought. So if you’re really at 90db averages, you might be risking speaker damage with highly dynamic music. There’s only so much a 5" driver can handle.

This is assuming anechoic or semi-anechoic conditions. With a couple db of wall gain they'll be less stressed. 

Power, thermal compression sets in far before you even approach the headroom limit of your Luxman. I know from experience owning Harbeth 30.2 that Harbeth speakers are just not meant to be played loud. Continuous spl levels of above 90dB will lead to a very compressed soundstage and audible resonance from the cabinent in the lower bass frequencies. If you want louder you absolutely must go to the 40.1 or better yet get a different speaker...