To find the number of distinct proper subsets of a set, we need to consider that a proper subset is a subset that includes some, but not all, of the elements of the original set.
The set N = {2, 50, 62, 13, 40} contains 5 elements. For each element, we have two choices: include it in a subset or exclude it. This means that for each element, there are 2 possibilities: it can be in the subset or not in the subset.
Therefore, the total number of distinct subsets of a set with 5 elements is 2^5, which is equal to 32.
However, since we are looking for proper subsets, we need to exclude the empty set and N itself from the count. So, the total number of distinct proper subsets of the set N = {2, 50, 62, 13, 40} is 32 - 2 = 30.