Help with P-channel mosfets
You have the P-MOSFET connected wrong. The Source (S) terminal should be toward the 5V and the Drain (D) should connect to the LED in your diagram.

The condition where the P-MOSFET will be off is if the voltage between the Gate (G) and the Source (S) is less than the VGSTHR.

The reason that the LED lit up in your drawn configuration is because the body diode was forward biased and letting current pass from the D terminal to the S terminal.