Your calculations are correct but my guess is that there is current limiting designed into that diode.
...You are fine just giving it 5V and 27mA makes it nice and bright.
yep just use ohms law figure for fwd voltage of the diode.
Better yet get an SMD one and take the one off and replace with the value you want... for a soldering challenge!
You'll pay more in postage
Buying just one component. Wow - that's a new concept for me.
although, a n00b quickly learns to buy *two* ) to cover any silly error or bad soldering technique !