You should have no problems at 300 with a 1.5x5. Allot of folks think a fixed 4 or 6 are more are great on a big game rifle and shoot longer ranges than 300. All my goto coyote guns have 1x4 or 1.5x6 scopes on them and I have no problems out to 300+.
On something like a 375 I'd be more concerned about having more FOV for the fast close in shot than the long shot.
Once you get used to shooting a low power variable you find out how little magnification it takes to make good shots. My longest shot on a coyote this year was right at 200 yrds and I didn't have time to turn the scope up and shot him at 1.5x.
Got him out by the power poles. Even in this terrain I was comfortable with the 1.5x6 on my 6mm/204.
Minox makes a 1.5x8 that would be real handi also. With a 60' FOV on the bottom end, great glass , a 32mm objective and under $400 whats not to like.
Here's a target shot with a very old El Paso Weaver 4x at 300 yrds.
