Microcontroller PWM LED strips driver with N-channel MOSFET
You can forget about the PSMN2R8-80BS without an additional stage, at 3V3 it is high impedance (see Fig. 9).
The FDS on the other hand looks promising, it will be in the range of 20 to 30 m\$\Omega\$ (see Fig. 2). At a current of 5 A, the voltage drop will be below 0.15 V.