Every element $k \in A$ has a unique representation $k = 5^x \cdot s$ where $s$ is not divisible by $5$ (and also not divisible by $2$ or $3$, from the problem statement). This number $s$ must be less than $30n$. The number of integers less than $30n$ which are not divisible by $2$, $3$ or $5$ is exactly $n \cdot \varphi(30) = 8n$ (specifically, these are the numbers with remainder $1,7,11,13,17,19,23,29$ mod $30$). Since $A$ has $8n+1$ elements, it follows that there are (at least) two elements of $A$ with "the same $s$", i.e. $a = 5^x \cdot s$ and $b = 5^y \cdot s$. Clearly one of these divides the other, and we are done. $\blacksquare$.