Understanding the problem:
To find the two positive integers whose difference is 2:5, we need to first understand what the term "difference" means in this context. The difference between two numbers is the result of subtracting one number from the other. In this case, the difference between the two integers is given as 2:5, which means that one number is 2 units less than the other.

Setting up the equation:
Let's assume the two integers are x and y, where x is 2 units less than y. This can be represented as:
y - x = 5 (since the difference is 2:5)
y = x + 2 (as x is 2 units less than y)

Solving the equation:
Substitute the second equation into the first equation:
x + 2 - x = 5
2 = 5
This is not possible, which means there is an error in our assumption.

Correcting the assumption:
Let's assume the two integers are x and y, where x is 5 units less than y. This can be represented as:
y - x = 5
y = x + 5

Solving the corrected equation:
Substitute the second equation into the first equation:
x + 5 - x = 5
5 = 5
This equation is true, which means our assumption is correct.
Therefore, the two positive integers are 5 and 10, as 10 - 5 = 5.