1. **Stating the problem:** Simplify and evaluate the expression $$\left(\frac{2\sqrt{2} - \sqrt{5}}{\sqrt{3}}\right)^{2023} \times \left(\frac{2\sqrt{2} + \sqrt{5}}{\sqrt{3}}\right)^{2023}$$. 2. **Rewrite the expression:** This is a product of two terms raised to the same power. We can combine the inside terms first: $$\left(\frac{2\sqrt{2} - \sqrt{5}}{\sqrt{3}} \times \frac{2\sqrt{2} + \sqrt{5}}{\sqrt{3}}\right)^{2023}$$ 3. **Multiply the numerators:** Using the difference of squares formula, $(a - b)(a + b) = a^2 - b^2$: $$\left(\frac{(2\sqrt{2})^2 - (\sqrt{5})^2}{(\sqrt{3})^2}\right)^{2023}$$ 4. **Calculate each term:** $$ (2\sqrt{2})^2 = 2^2 \times (\sqrt{2})^2 = 4 \times 2 = 8 $$ $$ (\sqrt{5})^2 = 5 $$ $$ (\sqrt{3})^2 = 3 $$ 5. **Substitute and simplify inside the parentheses:** $$\left(\frac{8 - 5}{3}\right)^{2023} = \left(\frac{3}{3}\right)^{2023} = 1^{2023}$$ 6. **Evaluate the power:** $$1^{2023} = 1$$ **Final answer:** $$1$$