[5.5] Move validated request input extraction into its own method

[Lidbetter]

For my project I want to tweak that from $request->only(...) to $request->all(...) I could just override both validateWith and validate methods, but I would rather separate them then only change the bit I care about.

Reasoning:
If either of those methods' internal logic change in the future, my overrides should still work.

The 3 lines I am extracting are duplicated in those two methods, I think there is some general benefit of putting them in a single method.