To solve this question it is necessary to know how many shots were taken to establish the current 0.80 probability of making the shot. For example, if the player established the 0.80 shooting percentage by making 240 out of 300 shots, then if he made his next 100 shots this would yield a 0.85 shooting percentage (340 made out of 400 attempted.) If instead, he previously made 60 out of 75, he would only need to make his next 25 shots to yield 85 out of 100. I see the pattern now.......the player must always make the next n shots where n is equal to 1/3 of the number of previously attempted shots. Since the number of shots attempted must be an integer, the 0.80 probability of making the shot must have been established over some multiple of 3 trails. Also 80% of this multiple of 3 must also be an integer. Thus, the minimum number of shots to make in order to convert a 0.80 probability into a 0.85 probability is 5 with the original number of shots attempted was 15 (with 12 converted). By making the next 5, the player will now have made 17 out of 20 shots which is 85% or 0.85. In mathematical terms, the player must make his next x shots where x is equal to one-third of the number of shots attempted to establish the 0.80 average initially. Of course, if the 0.80 probability of making the shot was established by making 24 out of 30 attempts, then if the next 10 shots are made, this would become 34 made out of 40 attempted which is 0.85.