1. Stating the problem: Simplify the expression $\sqrt{5} \times \sqrt{11}$. 2. Formula used: The product of square roots rule states that $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. 3. Applying the rule: $$\sqrt{5} \times \sqrt{11} = \sqrt{5 \times 11}$$ 4. Simplify the multiplication inside the square root: $$\sqrt{55}$$ 5. Final answer: The simplified form of $\sqrt{5} \times \sqrt{11}$ is $\sqrt{55}$.