Voltage doesn't really matter that much with LEDs actually. You could give the LED 30V as long as you limit the current to it. For my application I am running the LEDs in series which means that for each additional LED you need at least that much more voltage to get the diode to light up. I ended up giving my array of 5 LEDs about 22V. If you know how to read current with your multimeter, here is an experiment so that you can see what I'm talking about:
Take 5v and hook up an LED like you mentioned with a resistor, now put the multimeter in series with the LED and you should be able to read the current, you'll know your reading it when you light lights up, then you will get a reading at the same time. If you don't know what it means to hook it up in series then google it first, likewise with how to read current on your multimeter. Finally change your multimeter back to read DC voltage and put one end on the positive line of your source 5v while putting the other end on your negative line with the resistor attached. How much voltage do you get? Should still be right at 5v. That is the long explanation to what a CURRENT limiting resistor does.