1. **State the problem:** Simplify the expression $$\frac{\sqrt{32}}{\sqrt{25}}$$. 2. **Recall the quotient property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$, where $a \geq 0$ and $b > 0$. 3. **Apply the quotient property:** $$\frac{\sqrt{32}}{\sqrt{25}} = \sqrt{\frac{32}{25}}$$ 4. **Simplify the fraction inside the square root:** $$\frac{32}{25}$$ is already in simplest form. 5. **Express the square root of the fraction as the square root of numerator and denominator:** $$\sqrt{\frac{32}{25}} = \frac{\sqrt{32}}{\sqrt{25}}$$ (which is the original expression, so we continue simplifying the numerator and denominator separately). 6. **Simplify $\sqrt{32}$:** $$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$$ 7. **Simplify $\sqrt{25}$:** $$\sqrt{25} = 5$$ 8. **Substitute back:** $$\frac{\sqrt{32}}{\sqrt{25}} = \frac{4\sqrt{2}}{5}$$ 9. **Final answer:** $$\boxed{\frac{4\sqrt{2}}{5}}$$