PL-OM 2017 Problem 4

Prove that the set of positive integers $\mathbb Z^+$ can be represented as a sum of five pairwise distinct subsets with the following property: each $5$ -tuple of numbers of form $(n,2n,3n,4n,5n)$ , where $n\in\mathbb Z^+$ , contains exactly one number from each of these five subsets.