$-9<7 x^{2}+5 \leq 11$

Step 1 ：Given the inequality $-9<7 x^{2}+5 \leq 11$

Step 2 ：Rewrite the inequality as $7x^2 + 5 - 11 < 9$ and $7x^2 + 5 - 11 \leq 9$

Step 3 ：Simplify to $7x^2 - 6 < 9$ and $7x^2 - 6 \leq 9$

Step 4 ：Solve these inequalities separately to get $x = [-\sqrt{105}/7, \sqrt{105}/7]$

Step 5 ：The solutions to the inequalities are the same, which means the solution to the original inequality is the interval between these two values, inclusive

Step 6 ：\(\boxed{x \in \left[-\frac{\sqrt{105}}{7}, \frac{\sqrt{105}}{7}\right]}\)