We start with the numbers from 1 to 5. Take any two of them, which we will call a and b. Replace a and b with ab+a+b. If you chose 2 and 4, that would give 2*4+2+4= 14, so we have left:
14 1 3 5. Choose another two numbers and continue this process until there is one number left.

Using my powers of concentration, I can tell you in advance that the number you end up with is 719. What this means, of course, is that the order in which the numbers are chosen does not matter. The question is why? Can you come up with a simple formula for the final number?

There is nothing special about the numbers 1 to 5. If we had chosen any group of numbers, the final answer would be independent of the order in which the numbers are chosen.