You've got them backwards. The 20th percentile would be the level below which only 20% of the observations fall. Since 80% of the scores fall below A's score (four out of 5), then A is in the 80th percentile. Since 20% of the scores fall below D's score, then D is in the 20th percentile, not the 80th. See Wikipedia's page on percentiles (it's rather rough, but the lead will do it).
Edit: You edited the question, so here goes the answer to that:
It seems that you are not really asking about percentiles, but about percents. They are not the same thing. A is in the top 20 percent, but not "the top 20 percentile". By definition, percentile refers to how many quantities are below. It makes no sense to talk about "top 20 percentile". Your intended question is about percents, not 'percentiles'.
To answer that: You have 5 people; A is the top, B and C are tied in second, D is in fourth, and E in fifth. A is certainly in the top 20% of the group, E in the bottom 20%; D and E are in the bottom 40%. A, B, and C are in the top 60% (not the top 40%); B, C, D, and E are in the bottom 80%. But you are using "percentile" wrong. If X is in the 40th percentile, then that means that 40% of the scores are below him; that would mean he is at the bottom of the top 60%. A is in the 80 percentile, B and C are in the 40th percentile, D is in the 20th percentile.