In the first act of a play, all the actors were on stage. the second act opened with 1/2 the actors on stage, and then 5 actors left. after that, 1/2 the remaining actors left

This is a matter of number sequencing. You might think of arithmetic progression, geometric progression or harmonic progression. They don't apply to this problem. The mentioned progression have a common pattern that is used all throughout the sequence. For this problem, there is no pattern. So, we just ave to follow the flow as instructed.

For the first act, there are x actors. During the second act, it becomes 0.5x. During the third act, 5 actors are removed, that leaves us with 0.5x - 5. In the last act, only half of the actors remained again. That leaves as with (0.5)(0.5x - 5).

If the question is, how many actors were left by the end of the acts, the answer would be 0.5(0.5x - 5). We can't answer in exact numbers because the total number of actors x were not specified.