Yes, indeed. The rule of thumb is that hard to start machines, like band saws, lathes, and other stuff that needs to spin up to speed, typically require 1.5HP to start, so 4.5HP in theory should start the lathe. But there are a lot of factors, the power in your shop, how difficult the machine is to start up, etc...motors vary also, but in general, yes a 5HP motor will start a 3HP lathe.
I'm not sure what happened to Rod over on PM, it's been a while now...but he used to hang out on the Home Gunsmith forum. I was looking for Rod, and renewed my membership, but Rod doesn't use that forum anymore. Someone did steer me to his YT channel, but he doesn't post too much these days, not like when he moderated the Gunsmithing forum on PM.
With all this talk of lathes, I will put myself out on a limb and say that a mill is MUCH more useful to do gunsmith work. Sure, you need a lathe to chamber and cut threads, but it seems to me that most gunsmiths use their lathes for truing actions and threading muzzle devices. Pretty much the rest of it, including drilling, can be done on a mill. Any serious gunsmith will have both.
I agree, anyone would be lucky to get one of his machines. Years ago I saw a post of his using a Skinner 9xx 4-1/2" chuck, they're one of the best vintage chucks in a small size. Nowadays they're very hard to find, but come up occasionally...unfortunately people asking $200+ for them nowadays...

I more often use an 8" chuck, but have 6" and 4" solutions as well.
A good reminder for all. Whatever lathe you get, you will end up spending more money on tooling that you spend on the lathe, or at least you should plan on it. Even if you get tooling with your lathe, it's most often not the tooling you need...Murphy's Law. DAMHIKT