Conditional Variance of a Surviving Exponential

Let $X \sim \operatorname{Exp}(\lambda)$. Using the memoryless property, find $\operatorname{Var}(X \mid X > t)$ for $t > 0$. Does conditioning on survival change the variance compared to $\operatorname{Var}(X)$? Evaluate numerically for $\lambda = 5$ and $t = 2$.