1. **State the problem:** Simplify the expression $$\sqrt{x^5} \times \sqrt{x}$$. 2. **Recall the property of square roots:** For any non-negative $a$ and $b$, $$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$. 3. **Apply the property:** $$\sqrt{x^5} \times \sqrt{x} = \sqrt{x^5 \times x}$$ 4. **Multiply the powers of $x$ inside the square root:** $$x^5 \times x = x^{5+1} = x^6$$ 5. **Rewrite the expression:** $$\sqrt{x^6}$$ 6. **Simplify the square root of a power:** $$\sqrt{x^6} = x^{\frac{6}{2}} = x^3$$ 7. **Final answer:** $$x^3$$ This simplification assumes $x \geq 0$ to keep the square root defined in the real numbers.