Five integers between 10 and 99, inclusive, are to be formed by using

I get the logic here that to minimize the sum of the five integers, we will make the tens digits as smallest possible which means we'll use 1, 2, 3, 4, and 5 as the TENS digits and use the other five possible digits (0, 6, 7, 8, and 9) for the UNITS digits. However, how do we know that the sum of all possible combinations of 5 two-digit numbers will be the same, ie 180? While attempting this question, I marked 50 because I did not calculate if other combinations where the largest two-digit number is 59 yield the same sum, ie 180. My question then becomes at what point do we decide that let me try to sum up other combinations as well to see if they give the same sum or a larger sum? I assumed that the combination with 50 the largest number, the sum will be minimum. Is it just a miss on my end of not checking all the cases (doing this in time constraints), or it is something we intuitively derive by looking at the possible combinations that it might be worth checking if all combinations give the same sum?­