The IRFR3708 has a worst-case on-resistance of 0.03 ohms at Vgs=2.8, so at about 5A it will dissipate 0.75W
which is feasible for a large surface mount package. So yes, a good choice.
Note that the crazy 61A figure is only possible as a pulse rating if the gate drive is at least 5V - its beyond
anything the package or a PCB trace could handle continuously, and probably will cause premature failure
of the bond wires even as low-duty-cycle pulses. IR at their marketing games again.