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The .375 H&H is a very forgiving cartridge. Various powders will work. You have not specified what type of bullet (s) you will be using and what applications you have in mind. For the 250-270 grainers Reloder 15 is usually a good choice. 285's as well. For 300 grainers, Winchester 760 has many proponents as do the 4350's. IMR 4064 works well with all bullet weights.
4350 and other med to slow burning is fine for heavy loads that will recoil. 4064 , and reloader 15 are good for lighter loads but still lots for whats out there to shoot.
4895 also used by some, I like the ones I first mentioned...
I have loaded for many a .375 H&H and found 80 grains of winchester 760 with 300 grain bullets was always a very accurate and velocity is near the max possible.
Looking into the newest manuals of nosler, barnes and 4 edition of hornady, they all list H4895 powder and the velocity is good in all three books. Unless you reload for a few other cartriges this might be one to consider.
Keith
I've used IMR4064, WW760, RL15 and IMR4350, all with very good results.
I think the .375 H&H is the most 'accommodating' cartridge ever invented. It wouldn't surprise me to hear that somebody is getting sub-moa groups with 68 gr. of Cream of Wheat.