Do you know what forward voltage the LEDs are designed to work at? The current rating looks OK and 80 ish Ohms is in the right sort of ballpark, but you need to know the LED required voltage to know for sure.
If you have the correct resistor, and the LED is rated as you say and connected the right way round, you should be able to apply 5V to the LED and series resistor and it will light up. For example, you could just touch the wires to the 5V and ground pins on the Arduino regardless of any sketch.
If that doesn't work, either the 5V supply isn't producing 5V, or the LED is not the rating you think it is or has failed or is connected back to front, or the series resistor is not the resistance you think it is or has failed, or you have connected them wrongly.