since the load/rpm is going to be the same I would expect that going to the 5S I would just get a lower amp draw.

Yes you will, but you will also need more cells. All of that and also its weight is linear, so what you save on draw, you must give on voltage = cells and thus the power is the same, and at the same time also Wh is the same so it means also weight is the same.

IF the efficiency is the same. But since you will need whole system throttled down, you will rpobably loose little bit of efficiency, so probably final solution will be little heavier, or at the same weight it will fly probably some seconds shorter :- ))

Thal lower efficiency means some heat somewhere, I guess it will be on ESC, it will probably heat more than if you fly with more open throttle - so the solution will be ESC for higher currents and thus again heavier :- ))