1. **Problem statement:** Given a random variable $X$ with expected value $E[X] = 5$ and variance $\text{Var}(X) = 2$, find $E[X^2]$. 2. **Recall the formula for variance:** $$\text{Var}(X) = E[X^2] - (E[X])^2$$ This formula relates the variance, the expected value of the square of $X$, and the square of the expected value of $X$. 3. **Rearrange the formula to solve for $E[X^2]$:** $$E[X^2] = \text{Var}(X) + (E[X])^2$$ 4. **Substitute the given values:** $$E[X^2] = 2 + 5^2 = 2 + 25 = 27$$ 5. **Interpretation:** The expected value of the square of $X$ is 27. **Final answer:** $$E[X^2] = 27$$