Fallout 4 is badly optimized, and there are some spots in the game where you will dip into the 40s pretty much regardless of what CPU you have. I ran into the same problems with my 6600k, so moving to another i5 isn't the answer. The game does show decent gains going from an i5 to an i7 in benchmarks, making it one of the few titles to really benefit from hyperthreading, but even then framerate drops have been reported with i7 systems as well.
In terms of improving performance, make sure God Rays are set to low or off, the higher settings kill performance. Dropping shadow quality sometimes also helps, especially since the higher presets seem to draw a ton of shadows you can't actually see.