1. **State the problem:** Simplify the expression $$5^7 \div (5^2 \times 5^3)$$. 2. **Recall the laws of exponents:** - When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$. - When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Simplify the denominator first:** $$5^2 \times 5^3 = 5^{2+3} = 5^5$$ 4. **Rewrite the original expression:** $$5^7 \div 5^5$$ 5. **Apply the division rule:** $$5^{7-5} = 5^2$$ 6. **Final answer:** $$5^2 = 25$$