Here's how to simplify the expression: Step 1: Identify common factors in the numerator. The numerator is $5^n - 5^{n-2}$. We can factor out $5^{n-2}$. Recall that $5^n = 5^{n-2} \cdot 5^2$. $$ 5^n - 5^{n-2} = 5^{n-2} \cdot 5^2 - 5^{n-2} \cdot 1 = 5^{n-2}(5^2 - 1) $$ $$ 5^{n-2}(25 - 1) = 5^{n-2}(24) $$ Step 2: Identify common factors in the denominator. The denominator is $5^3 \times 5^n - 125 \times 5^{n-2}$. First, calculate $5^3$: $5^3 = 5 \times 5 \times 5 = 125$. Substitute this value into the denominator: $$ 125 \times 5^n - 125 \times 5^{n-2} $$ Now, factor out $125$: $$ 125(5^n - 5^{n-2}) $$ From Step 1, we know that $5^n - 5^{n-2} = 5^{n-2}(24)$. Substitute this into the denominator: $$ 125 \cdot 5^{n-2}(24) $$ Step 3: Substitute the simplified numerator and denominator back into the fraction. $$ \frac{5^{n-2}(24)}{125 \cdot 5^{n-2}(24)} $$ Step 4: Cancel out common terms from the numerator and denominator. Both the numerator and denominator have the term $5^{n-2}(24)$. $$ \frac{\cancel{5^{n-2}(24)}}{125 \cdot \cancel{5^{n-2}(24)}} = \frac{1}{125} $$ The simplified expression is: $$ \boxed{\frac{1}{125}} $$