1. **Problem:** Simplify the expression $5^{1/3} \times 5^{2/3}$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** $$5^{1/3} \times 5^{2/3} = 5^{(1/3 + 2/3)} = 5^{3/3} = 5^1$$ 4. **Simplify:** $$5^1 = 5$$ 5. **Answer:** The simplified form of $5^{1/3} \times 5^{2/3}$ is $5$.