What type of deer are you thinking? The idea of shooting and killing deer cleanly at 500m with a 375 h&h is going to depend more on bullet choice and the size of the deer than just the scope magnification. A fallow deer at 400m or 500m m is going to offer little resistance to a 375 bullet and it will likely not expand sufficiently to kill quickly. A sambar stag or a Wapiti bull are big enouigh to justify the use of such a big-holed rifle. Speer used to make a 235grn bullet specifically for deer.
The other consideration is shooting light. A Cape buffalo will probably be shot when there is bright light. An old sika or red might come out right on last light and that's when a 3-9x40 beats a 1.5-5x hands down. Maybe a good compromise is a Leupy 2.5-8x36. They are pretty good on last light, small, light, and handle recoil well.
Rifles are cheaper than they ever have been, it's a buyer's market now. Why not own a dedicated deer rifle? Put the 3-9x on that and a low power scope on the 375h&h?
Just some musings....
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