Do I need a regulator with a standard 5V wall adapter?
Measure the no-load voltage with a meter and then measure it with full load. If the two voltages are both about 5V +/- 0.5 volts you may get away without a regulator (and that's if you need a 5V supply to your PIC). You might also need to add extra decoupling capacitors to avoid too much ripple or switching noise from the internal regulator it may use.