5. (10 points) If $\frac{O}{11}<\frac{7}{\square}<\frac{4}{5}$, then the maximum sum of the non-zero natural numbers that can be filled in “ $O$ ” and “ $\square$ ” is

保留源文本的换行和格式，翻译结果如下：

5. (10 points) If $\frac{O}{11}<\frac{7}{\square}<\frac{4}{5}$, then the maximum sum of the non-zero natural numbers that can be filled in “ $O$ ” and “ $\square$ ” is
5. (10 points) If $\frac{\bigcirc}{11}35$, then $\square \geqslant 9$;
$\frac{0}{11}$ and $\frac{7}{\square}$ have a common denominator: $\frac{O \times \square}{11 \times \square}<\frac{77}{11 \times \square}$

So, $\bigcirc \times \square<77$,
Then, the maximum product of $\bigcirc \times \square$ is 76,
To maximize the sum of “ $\bigcirc$ ” and “ $\square$ ”, the difference between the two numbers should be maximized,
$$
76=1 \times 76,
$$

Therefore, when $\bigcirc=1, \square=76$, the sum of the two numbers is maximized,
That is, $\bigcirc+\square=1+76=77$.
Answer: The maximum sum of the non-zero natural numbers that can be filled in “○” and “ $\square$ ” is 77.
Hence, the answer is: 77.