Hi,
that sounds strange.
The number plate light is normally a red wire that is connected to the red wire going to the right side rear light so it doesn't make sense to me that that what is down the end of one red wire is affecting what it at the end of another red wire. A LED is just a diode that glows, and a diode is something that acts like a one-way valve so the flow of the current only travels in one direction. So it could be related to your problem, but I can think of how you would have things wired that allows the tail light LED to work and the numberplate light to not work.
The bulb will be 5W, not 5V, you are mixing voltage with wattage. A 12V/5W bulb is the correct one for tailights and number plate lights. No resistors should be needed.
Terry