To find the largest possible value among the numbers, we need to understand the concept of the arithmetic mean and the properties of natural numbers.

Arithmetic Mean:
The arithmetic mean, also known as the average, is calculated by summing up all the numbers in a set and dividing the sum by the total number of elements in the set. In this case, the arithmetic mean of five different natural numbers is given as 12.

Properties of Natural Numbers:
Natural numbers are positive integers starting from 1 and extending to infinity. Each natural number is greater than the previous one.

Finding the Solution:
To find the largest possible value among the numbers, we need to consider the properties of natural numbers and the given arithmetic mean.

1. Assume the numbers are a, b, c, d, and e.
2. Since the numbers are different natural numbers, they must be consecutive. Therefore, we can assume the numbers as x, x+1, x+2, x+3, and x+4, where x is a natural number.
3. The arithmetic mean is given as 12. Thus, we can write the equation as (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5 = 12.
4. Simplifying the equation, we get (5x + 10) / 5 = 12.
5. Further simplifying, we have 5x + 10 = 60.
6. Subtracting 10 from both sides, we get 5x = 50.
7. Dividing both sides by 5, we have x = 10.
8. Therefore, the numbers are 10, 11, 12, 13, and 14.
9. Among these numbers, the largest possible value is 14.

Therefore, the correct answer is option 'C' - 50.