If the five volt High comes from a PIC pin, then it can source ~20mA. To get from 20mA to 3000mA, that takes a β of 3000/20 = 150 which is hard to do with a single NPN. Use either a Darlington, a Darlington-connected pair of of NPN transistors, or a logic-level NFET. Connect the emitter/source to the same voltage as the PIC Vss, connect the Collector/Drain to the negative lead of the Servo, connect the positive lead of the Servo to +5V. If using NPNs, you will need a current-limiting resistor between the PIC pin and base of the transistor.