Memorylessness Breaks for Exponential Mixtures

Let $X$ have the mixture density $f(x) = \frac{1}{2}e^{-x} + \frac{5}{2}e^{-5x}$ for $x \geq 0$ (a $50{-}50$ mixture of $\operatorname{Exp}(1)$ and $\operatorname{Exp}(5)$).

(a) Compute $P(X > s + t \mid X > s)$ as a function of $s$ and $t$, and show it depends on $s$ (i.e., the memoryless property fails).

(b) Evaluate $P(X > 2 \mid X > 1)$ and compare with $P(X > 1)$.

(c) Interpret: given that $X$ has survived past $s$, how does the conditional distribution change as $s$ increases?