1. **State the problem:** Simplify the expression $5^{-2} \cdot 5^{3}$ using the properties of exponents. 2. **Recall the property of exponents:** When multiplying powers with the same base, add the exponents: $$a^{m} \cdot a^{n} = a^{m+n}$$ 3. **Apply the property:** $$5^{-2} \cdot 5^{3} = 5^{-2+3}$$ 4. **Simplify the exponent:** $$5^{1}$$ 5. **Final answer:** $$5$$ The expression simplifies to 5.