1. Stated problem: Calculate $5^3 \div 5^3$. 2. Use the quotient rule for exponents: $a^m \div a^n = a^{m-n}$. Here, $a=5$, $m=3$, and $n=3$. 3. Apply the rule: $5^3 \div 5^3 = 5^{3-3} = 5^0$. 4. Any non-zero number raised to the zero power is 1. So, $5^0 = 1$. Final answer: $1$.