Ok, I found a few STW55NM50N laying around, and I'm thinking that they're better suited than the STW75NF30 to be driven at 5V:
What do you think?

Note that the graphs are usually drawn using typical values..

 

Very hard to judge from that graph but it appears the typical voltage with Vgs = 5V and Id = 20 A is around 3 volts, or three times worse.

 

Never mind... I'm convinced that most mosfets out there are designed for full-conduction (if that's the correct term) when at least 10V is applied at the gate.

Since what I'm doing is rather important, I decided to add a DC-DC converter to the circuit, even though it's a little expensive.
On the plus side, said converter outputs power with an isolated ground.