1. **State the problem:** Simplify the expression $$\frac{e^{\ln 5}}{e^{\ln 6}}$$. 2. **Recall properties of logarithms and exponents:** For any positive number $a$, $e^{\ln a} = a$ because the exponential and natural logarithm functions are inverses. 3. **Apply this property:** $$\frac{e^{\ln 5}}{e^{\ln 6}} = \frac{5}{6}$$ 4. **Final answer:** The simplified form of the expression is $$\frac{5}{6}$$.