The digits 1, 2, 5, 6, and 9 are all used to form five-digit even numbers, in which no digit is repeated. The difference between the largest and smallest of these numbers is
(A) 83916
(B) 79524
(C) 83952
(D) 79236
(E) 83016
To get the largest possible number by using the digits $1,2,5,6$, and 9 exactly once, we must choose the largest digit to be the first digit, the next largest for the next digit, and so on. Thus, the largest possible number is 96521 .

Also, using this reasoning, there are only two numbers that use these digits which are at least 96500 , namely 96521 and 96512 .

Therefore, 96512 must be the largest even number that uses each of these digits exactly once. Reversing our logic, the smallest possible number formed using these digits is 12569 , and the only other such number smaller than 12600 is 12596 , so this must be the smallest even number formed using these digits.

Calculating the difference, we get $96512-12596=83916$.

ANSWER: (A)