There are chargts & guides but crank length (like pretty much anything else to do with bike fit) is not an exact science. 175mm cranks have become so common purely because they fit so many people. At 5'10" with your inside leg a 175mm will be doing you just fine. I'm 6'3" and the shortest crank I ever ran was on my singlespeed at 172.5mm.

Using a crank just that little bit shorter meant that I was pushing ever so slightly harder which meant I spent less time not pedaling.

The longer the crank arm the greater the leverage and the (relatively) easier it is to push a big gear. I hope that makes sense

175mm will do him fine but 172.5mm would be better

depending on relative length of thigh & calf and myriad other things that we can't see here

Exactly.