[tex]5:\sqrt{5} = \sqrt{25}:\sqrt{5} = \sqrt{25:5} = \sqrt{5}\\\\\frac{5}{\sqrt{5}} = \frac{5}{\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{5} = \sqrt{5}\\\\\sqrt{25:5} = \sqrt{5}\\\\\frac{\sqrt{25}}{\sqrt{5}} = \sqrt{\frac{25}{5}} = \sqrt{5}\\\\\sqrt{25}:\sqrt{5} = \sqrt{25:5} = \sqrt{5}\\\\\\\boxed{\sqrt{5} = 5:\sqrt{5}=\frac{5}{\sqrt{5}}=\sqrt{25:5} = \frac{\sqrt{25}}{\sqrt{5}}=\sqrt{25}:\sqrt{5}}[/tex]
