You require a resistor with an LED, regardless of the voltages used.
Put simply, an LED is a semiconductor junction device. A semiconductor junction device always has a voltage drop, but doesn't have any internal resistance.
In other words, it will drop a specific amount of voltage in a circuit, but it will not affect the current flow.
Using Ohm's law, we know that I=V/R - the current is the voltage divided by the resistance. We have a known voltage - the supply voltage, 5V. Semiconductor junction devices have no resistance, so the resistance is 0.
Simple maths: I=V/R = 5/0.
What is 5 divided by 0? It's a bang, that's what.
Anything divided by 0 is infinity. That's infinity amps being drawn out of the Arduino IO pin - the pin that can only supply up to 40mA. Poor pin.
So you have to add some resistance to make up for the lack of resistance in the LED.
So remember kids - an LED with no resistor is like a short circuit.