I confess that I did not look at the PIC device being used, but if RC5 is a standard pin (can be 5V or 0V and can sink or source current) then I think if you measure the circuit being proposed, you will see the transistor really is not doing anything - in fact, it will be on at all times.
Instead you need an NPN transistor. The base gets connected directly to RC5, The collector to 9V and the emitter to the LED Anodes. This limits the voltage seen by all PIC pins to 5V or less (closer to 3V), and supplies the current from 9V (The PIC still needs to sink that current)
You may well damage the PIC trying out the circuit shown in the drawing.