So you need more than 3V and a total current of 500 * 20mA = 10A. A transistor switch can be used but the 2N2222 is only rated to carry 0.8A maximum so it is far too small to do the job.
The best technical solution is to use the 7805 to power the PIC and to use the voltage BEFORE the 7805 to power the LEDs through suitable resistors. All the LED cathodes would be joined together and a MOSFET connected to ground would be used to switch them. You can drive the MOSFET directly from the PIC or better still, use your 2N2222 between the PIC and MOSFET to boost the gate voltage.
It may be possible to wire some of the LEDs in series then the series chains in parallel but we need to know more about your power supply before we can advise the best way to do it.
Brian.