48X15!

Set a map: P(n) = 16 - n (n= 1, 2, ... 15), and P(M) = {P(a11), P(a12), ...} for all 5x3 tables.

{P(M): M} is an rearrangement of the original 15! tables.

Consider table M and P(M), the smallest row becomes the largest row, and the sum is 48.