[tex]5-\sqrt{27}x \leq \frac{5\sqrt{12}}{6}x-\frac{1}{3}\\\\5-\sqrt{9\cdot3}x \leq \frac{5\sqrt{4\cdot3}}{6}x-\frac{1}{3}\\\\5-3\sqrt{3}x \leq \frac{5\cdot2\sqrt{3}}{6}x-\frac{1}{3}\\\\5-3\sqrt{3}x \leq \frac{10\sqrt{3}}{6}x-\frac{1}{3}\\\\5-3\sqrt{3}x\leq \frac{5\sqrt{3}}{3}x-\frac{1}{3} \ \ /\cdot3[/tex]
[tex]15-9\sqrt{3}x\leq 5\sqrt{3}x-1\\\\-9\sqrt{3}x-5\sqrt{3}x \leq -1-15\\\\-14\sqrt{3}x \leq -16 \ \ /:(-14\sqrt{3})\\\\x \geq \frac{16}{14\sqrt{3}}\\\\x \geq \frac{16\cdot\sqrt{3}}{14\sqrt{3}\cdot\sqrt{3}}\\\\x \geq \frac{16\sqrt{3}}{14\cdot3}\\\\x \geq \frac{16\sqrt{3}}{42}\\\\\boxed{x \geq \frac{8\sqrt{3}}{21}}[/tex]
[tex]\underline{x \in \langle\frac{8\sqrt{3}}{21};+\infty)}[/tex]
