To simplify the expression \( \frac{5^6}{5^3} \) using the quotient rule of exponents, we can apply the rule which states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case:
\[ \frac{5^6}{5^3} = 5^{6-3} = 5^3 \]
So, the simplified expression is \( 5^3 \).
The correct response is 5^3.