Classes A and B each have 40 students taking a mathematics exam (total score 100 points). After the exam, classes A and B adjust their scores using $y_1 = 0.8x_1 + 20$ and $y_2 = 0.75x_2 + 25$ respectively, where $x_1, x_2$ represent the original exam scores of classes A and B, and $y_1, y_2$ represent the adjusted scores of classes A and B. The average adjusted scores for both classes are 60 points, with adjusted standard deviations of 16 and 15 points respectively. Select the correct options.
(1) Every student in class A has an adjusted score not lower than their original score
(2) The average original score of class A is higher than that of class B
(3) The standard deviation of original scores in class A is higher than that in class B
(4) If student A from class A has a higher adjusted score than student B from class B, then A's original score is higher than B's original score
(5) If the number of students in class A with adjusted scores below 60 (failing) is greater than the number in class B, then the number of students in class A with original scores below 60 must be greater than in class B