The probability of 1 not winning is 4/5, then the probability of the second person not winning is 3/4, and then the probability of the third person winning is 1/3.
So the probability is 4/5*3/4* 1/3= 1/5.
Another solution:
If the 1 person, the second person, the third person, the fourth person and the fifth person are drawn as an event, then the probability of these five events is equal, and one of them will happen, so the probability of the third person drawing the movie target is 1/5.