You're misunderstanding the circuit a bit.
Q1/R1 is basically a constant current sink, pulling down the gate voltage of the PMOS to around 3.5 V.
R2 is irrelevant as long as it's larger than R1. It's there for helping the PMOS turn off when the control input goes to 0 V. The way the circuit is drawn doesn't make this clear. It does not have influence on general operation.
Q3/R5 has already been explaind, but mawyatt's input is good, a base series resistor of around 200 ohms is sound design practice.