RU-ALLRUSSIAN 2018 Problem 117

Given a sequence of positive integers $a_1,a_2,a_3,...$ defined by $a_n=\lfloor n^{\frac{2018}{2017}}\rfloor$ . Show that there exists a positive integer $N$ such that among any $N$ consecutive terms in the sequence, there exists a term whose decimal representation contain digit $5$ .