pnp transistor basics
You say the collector of the PNP transistor is connected to +5V which is wrong, then show the emitter connected to +5V which is correct.
HFE is used for an amplifying transistor that always has plenty of collector to emitter voltage, not for a switching transistor that you want to saturate. The saturation spec for most transistors including the 2N3906 show a base current that is 1/10th the collecor current. So R1 should be (5V - 0.7V)/0.0007mA= 6143 ohms. Use 6.2k.