The riddle
How Many Times Can You Subtract 5 from 25?
Two answers, both fair
The riddle's answer is once. Take 5 from 25 and the result is 20, and the next time anyone subtracts 5 they are subtracting it from 20, not from 25. Read that way, the question asks how often 5 comes off the number 25 itself. The arithmetic reading differs. Subtract 5 over and over and you reach zero after exactly five subtractions: 25, 20, 15, 10, 5, 0.
The sums
25 minus 5 is 20, 20 minus 5 is 15, 15 minus 5 is 10, 10 minus 5 is 5, and 5 minus 5 is 0. That is five steps, matching 25 divided by 5. A sixth step would go below zero, to negative 5, which many everyday counting problems do not allow. Both answers hold, because the question uses "subtract from 25" in one sense and the arithmetic uses it in another.
Why the wording traps people
Most listeners go straight to division and say five. The riddle quietly points at a particular number, 25, and a number that has been changed is a different number. Once that is clear, the question is really about language, not about sums.
Try new numbers
Swap in other figures and the trick still works. How many times can 3 be subtracted from 12? Four by arithmetic, and once if the question means 12 itself. Ten from 100 gives ten steps or one, and every pair that divides evenly behaves the same way.