1. **State the problem:** Simplify the expression $$\frac{\sqrt{75a^5}}{\sqrt{3a}}$$. 2. **Use the property of radicals:** $$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}$$. 3. Apply this to the expression: $$\sqrt{\frac{75a^5}{3a}}$$ 4. Simplify inside the square root: $$\frac{75a^5}{3a} = 25a^{5-1} = 25a^4$$ 5. So the expression becomes: $$\sqrt{25a^4}$$ 6. Simplify the square root: $$\sqrt{25} = 5$$ and $$\sqrt{a^4} = a^{\frac{4}{2}} = a^2$$ 7. Therefore, the simplified expression is: $$5a^2$$ **Final answer:** $$5a^2$$