5. In the arithmetic sequence $\left\{a_{n}\right\}$, $a_{2}=5, a_{6}=21$, let the sum of the first $n$ terms of the sequence $\left\{\frac{1}{a_{n}}\right\}$ be $S_{n}$. If $S_{2 n+1}-S_{n} \leqslant \frac{m}{15}$ holds for any $n \in \mathbf{N}_{+}$, then the minimum value of the positive integer $m$ is $\qquad$.