Switch between 5V power supply and 6.6 battery

I want to use the following circuit for a switch between 5V power supply(Output of regulator7805)and 6.6 battery(4*1.65 AA) .

I want a low-cost mosfet for this circuit and current required for load is about 400-500 mA. What is suitable p-channel mosfet for this circuit?

The circuit has issues.

Since your battery voltage is greater than the 5V supply, the MOSFET body diode will
always conduct, so you've always be draining the battery...

You could reverse source and drain to solve that, but the 5V supply isn't going to be
enough to turn off the MOSFET as the gate voltage would have to be brought upto
the source voltage to turn it off, and now the source is at 6.6V.

I think a slightly more complex gate biasing arrangement using a zener and a couple of resistors
would be needed to fix this.

The circuit has issues.

Since your battery voltage is greater than the 5V supply, the MOSFET body diode will
always conduct, so you've always be draining the battery...

You could reverse source and drain to solve that, but the 5V supply isn't going to be
enough to turn off the MOSFET as the gate voltage would have to be brought upto
the source voltage to turn it off, and now the source is at 6.6V.

I think a slightly more complex gate biasing arrangement using a zener and a couple of resistors
would be needed to fix this.

So you say that if the voltage of the power supply is higher than the battery voltage, this circuit is suitable and If
the battery voltage is higher than the voltage of the power supply , I should reverse source and drain.Like This:

You think logic mosfet like FDN340P, not appropriate for this circuit?