1. The problem is to evaluate the expression $$\frac{\log_5 125}{\log_3 27}$$. 2. Recall the definition of logarithms: $$\log_b a = c \iff b^c = a$$. 3. Evaluate the numerator: $$\log_5 125$$. Since $$125 = 5^3$$, we have $$\log_5 125 = 3$$. 4. Evaluate the denominator: $$\log_3 27$$. Since $$27 = 3^3$$, we have $$\log_3 27 = 3$$. 5. Substitute these values back into the expression: $$\frac{\log_5 125}{\log_3 27} = \frac{3}{3}$$. 6. Simplify the fraction: $$\frac{\cancel{3}}{\cancel{3}} = 1$$. 7. Therefore, the value of the expression is $$1$$.