How do you replace the headlight bulb for low beam on a 2003 Mazda Protege 5?

You should check your owners manual. If you don't have it, then I can tell you.

If you have the bulb already, unplug the cord from the back of the headlight. Remove the sealing cover, a black rubbery ring that surrounds the bulb. You next need to unlatch the bulb retaining spring by pushing down on it, and then pulling it outwards. If done correctly, it should swing outwards, allowing you to pull out the bulb assembly. Once you have pulled out the bulb assembly, all you have to do is pull the headlight off of the thing that looks like it would be plugged into a wall outlet. Put the new bulb where the old one was, put the assembly back in the headlight, making sure that the headlight fits in properly and is aligned properly, swing the latch back around and lock it into place by first pushing down on the end of the retaining spring and then swinging it inward while still pushing downwards. Place the sealing cover back on, making sure it is on securely and that the arrow that is on the front is pointing upwards, and then plug the electrical connector back in and you should be good to go! Make sure to test it before you go driving.

One note: Don't touch the glass portion of halogen bulb with your barehands. The oils from your skin could cause the bulb to overheat when in use and explode.

See sources and related links below for bulb informaton.