Five different whole numbers, each greater than 0, have an average of 12. What is the largest that the greatest of the five can be?

The five numbers add to $5\times 12=60$. To leave as much as possible for the greatest, the other four must be as small as they are allowed to be, and being different whole numbers above 0 the smallest they can be is 1, 2, 3 and 4, adding to 10. So the greatest can be 60 - 10 = 50. 54 uses 0, 1, 2 and 3 for the other four, but 0 is not allowed - every number must be greater than 0. 60 gives the other four nothing at all, which no positive whole number can do. 14 assumes the five must be consecutive, 10 to 14, but nothing in the question forces that.