1. The problem asks to identify the rational numbers from the list: $-5$, $\sqrt{x64}$, $2.1$, $\sqrt{11}$, $\frac{2}{5}$, $2\pi$. 2. Recall that a rational number is any number that can be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. 3. Analyze each number: - $-5$ is an integer, which is a rational number because it can be written as $\frac{-5}{1}$. - $\sqrt{x64}$ seems to be a typo; assuming it means $\sqrt{64}$, which equals $8$, a rational number. - $2.1$ is a decimal that can be written as $\frac{21}{10}$, so it is rational. - $\sqrt{11}$ is an irrational number because 11 is not a perfect square. - $\frac{2}{5}$ is a fraction of integers, so it is rational. - $2\pi$ is irrational because $\pi$ is irrational and multiplying by 2 does not change that. 4. Therefore, the rational numbers are: $$-5, \sqrt{64} = 8, 2.1, \frac{2}{5}$$ 5. The irrational numbers are: $$\sqrt{11}, 2\pi$$