maximum reverse voltage applied to a resistor-LED configuration
The LED will definitely pass current in the reverse direction &mdash; nearly as much as in the forward direction. (Think of it as a 5-volt Zener diode.) This much current (and the heat that is produced) will definitely damage it, although probably not catastrophically.

The simplest solution is to put an ordinary diode in parallel with the LED, pointing the other way. This allows the reverse current to bypass the LED, limiting the reverse voltage across it to about 0.65 V, which is within its rating.

You can also use a second LED instead of a silicon diode, which will give you more light and reduce flicker, rather than letting the reverse current go to waste. The forward voltage of one LED will be less than the reverse rating of the other.