How not to waste power with digital inputs?
For the record, here's one of the circuits you tried:



Your problem is connecting the load to the source of the FET rather than the drain.
Tie the source directly to ground, and connect the load between 5 V and the drain:







simulate this circuit &ndash; Schematic created using CircuitLab

Now nearly all of the supply voltage can be applied to the load. In your proposal, the FET is working as a source follower, in which the FET will operate in saturation mode rather than fully switched, and voltage at the load is likely to be 2 or 3 V below the supply voltage.

If you want to have a high-side switch instead of low-side, use a PFET instead of NFET.