It makes no sense to shoot until the gun hurts you and you develop a flinch. Shooting 5 shot groups with a .375 won't tell you anything that you can't learn from shooting 3 shot groups, and once the rifle is sighted in, shooting pairs is a good drill. I don't envy the young guy who got tagged with the scope, and if the scope extends behind the cocking piece of the bolt, it should be moved forward. Some guys don't like this because they say they don't get a full sight picture at higher power settings. Me, I don't like being hit with the scope, and any critter you are going to smack with a .375 should be big enough that you don't need 10X to see it. A pal of mine with a .375 Ruger falls into this camp and he refuses to move the scope ahead despite being touched often and hit hard once. One of these days he'll throw that rifle up in a hurry and get badly cut. Back to recoil though, it is an acquired taste, and the more shooting one does with powerful rifles the more one can tolerate. Rifle fit becomes far more important, and if the pad is on the cheesy side it needs to be replaced.
I took a 21 year old kid out yesterday who had never fired a centerfire rifle before. We did some handgun shooting with my .357, .45 auto, and my .44, then I let him shoot my .375 Ultra. The first couple of rounds were off hand, then he shot from sitting and kneeling. No problem what so ever. The rounds were loaded pretty much to full steam with 270 gr Hornady's ahead of 100 grs of H-4831. I limited him to 8 or ten rounds in total, took time between each firing, and had him shoot pairs. He went away wanting more, and that's how it should be.