1. **State the problem:** Simplify the expression $5^6 \times 5^{-3}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** $$5^6 \times 5^{-3} = 5^{6 + (-3)} = 5^{6 - 3}$$ 4. **Simplify the exponent:** $$5^{6 - 3} = 5^3$$ 5. **Final answer:** $$\boxed{5^3}$$ This means the product simplifies to $5^3$, which equals 125 if you want the numerical value.