Is it possible to use a logic level mosfet as an external pass element with a 7805 regulator? All schematics I've found use a BJT instead.
To use a MOSFET, you need enough headroom to accommodate the MOSFET's threshold voltage and even with logic-level MOSFETs, you are talking about a ~2V minimum loss there instead of ~0.7V with a BJT. If the reason you want to use a MOSFET is to avoid the base current "losses," keep in mind that the BJT's base current does not make much of a difference efficiency-wise for a 7805 boost design since it goes through the 7805 and then the load so the BJT's Ibe does not make linear regulation significantly more wasteful than it already is and certainly not as wasteful as the extra 1.5-2.5V Vds drop across the PMOS due to Vgs.
With both the PNP and PMOS implementations all you need is a pull-up/bias resistor from supply to base/gate and 7805. If you want the 7805 to provide at most 500mA before the boost transistor kicks in, you will need ~1.5 ohms for PNP and ~3.3 ohms for the 2.5V PMOS assuming you can find a logic-level PMOS rated for the sort of continuous power you want to pass through it on its SOA graph. If your PMOS does not have a DC SOA curve, it cannot do linear regulation without considerable derating.
PMOS as a pass element for the 7805 can be done but it is more wasteful and likely more expensive than a PNP.