Everything looked original.

The bore diameter was probably greater than the nominal Proof diameter, perhaps about .358”.

It seemed to be accepted that you could use interchangeably both inside lubricated .360 No. 5 and outside lubricated .380 Long (.375 heel based bullets) in either rifle.

I believe most factory .360 No. 5 cartridges were made with hollow bases to get round the obvious problems of that approach.