A few factors drive my answer. Like, what am I shooting with the rifle? Is it PG or DG, large or small, etc. Some animals are significantly tougher than others. Some have smaller kill zones (i.e. Croc). Which bullet type and weight am I using? Barnes TSX for example likes velocity to expand well. Swift A-Frame might open up a bit better at lower velocities and others like Trophy Bonded even more likely to expand at lower speeds. My 375 is exceptionally precise. Sub moa at 100y and has recorded tiny groups out to 400y and at that range hit a 1/2" thick AR500 plate hard enough to bend it. But, with only a 1-6x optic, I have trouble accurately placing those groups exactly where I want at those extended distances.
Answer: I would not hesitate to shoot large PG animals like Zebra or Wildebeest out to 300y but the rifle is optimized for 200y and less and that is the sweet spot. That is with 300g TSX ammo. For almost any hunting rifle, I try to limit shots on game to the furthest range that still has 2000 fps velocity or higher in order to insure that the bullet reliably expands. I took a large Blue Wildebeest this year with the 375 at 160y. The bullet expanded to 2x the original diameter and penetrated about 3.5ft. That was enough for a kill shot. I did shoot it twice more at closer range to finish it quickly. Pics of two recovered slugs for visual reference. I would not hesitate to use it out to 200y with confidence. For DG all shots would be less than 100y. The first shot on Cape Buffalo would ideally be about 70-80y max which allows enough time to get in two or more followups should he charge and at least one if he runs away. This with 300g TSX or A-Frame ammo. On my last trip the longest shot I took with the 375 was 160y. Shots with my 308 ran from 20y for the shortest to 202y for the longest. All were 1 shot kills. Nothing ran over 60y after being shot. Most dropped right there or in a few steps.
For reference, we are prepping for a PG/DG hunt next year in Limpopo and Free State. The Free State shots can be longer ranging from 200-300y typical due to more open terrain on this concession, and can go out to about 400y. These longer shots challenge the 375 a bit. I will not use it at those longer distances for that reason. I can hit the 8" KZ with it at 400y but think it ill advised to hunt game with it that far out. For that reason, I am taking a nice old Husqvarna Swedish Mauser in 30-06 optimized for those longer shots. With 180g Swift Sciroccos it arrives at over 2000fps out to 400y and groups 2.25" for 3 shots at that range. The scope is a 3-16x FFP mil mil optic that allows me to dial my dope for a longer shot if needed. But out to 300y dialing is not really necessary. It only drops 1.4mil at 300y. Below is a pic of a three shot group at 400y for reference. A 300wm might be a better choice but the 30-06 will kill any PG I will be hunting on that trip. So, it is enough and the old Husky is more accurate than all but a full custom rifle and dead reliable.
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375HH 300g TSX Recovered - 2.0x and 2.2x expansion
400y grp 30-06 Husky