Yes, "2 miles East" and "3 miles Northeast" can serve as a basis for 2D displacements (i.e. displacements in a plane), since these are two non-parallel directions.

Then "5 miles north"

= "5 miles West" + "√50 miles Northeast" SKETCH IT!

= (-5/2) "2 miles East" + (√50/3) "3 miles Northeast".

So the components of "5 miles North" in the basis ["2 miles East", "3 miles Northeast"] are [-5/2, (√50)/3].