1. **State the problem:** Simplify the expression $$\frac{\sqrt{15}}{5\sqrt{20}}$$. 2. **Rewrite the denominator:** Note that $$\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}$$. 3. **Substitute back:** The expression becomes $$\frac{\sqrt{15}}{5 \cdot 2 \sqrt{5}} = \frac{\sqrt{15}}{10 \sqrt{5}}$$. 4. **Simplify the fraction:** Use the property $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$ to write $$\frac{\sqrt{15}}{\sqrt{5}} = \sqrt{\frac{15}{5}} = \sqrt{3}$$. 5. **Final simplified form:** Therefore, $$\frac{\sqrt{15}}{10 \sqrt{5}} = \frac{\sqrt{3}}{10}$$. **Answer:** $$\boxed{\frac{\sqrt{3}}{10}}$$