At the frequency of 5 MHz, the period of the oscillations is 1/5meg. That's a period of 1/5 microsecond.
There are 5 full cycles in one full microsecond, and there are 2.5 full cycles in a 0.5 us pulse.
You'll have to decide for yourself how damped a pulse of 2.5 cycles is, because the parameters of the definition are corrupted in the question.