Exponential distribution is memory less. So how many miles car has already travelled doesn't matter. Let $X$ be the event of car number of miles car travels before dying out.
So mean $\theta=10000$
$\begin{array}{ll} \text{Now } P(X>t) & = e^{-\frac{t}{\theta}} \\ \text{Since }P \bigg( X>\frac{x+y}{X>x} \bigg) &=P(X>y) \\ P(X>5000) &=e^{-\frac{5000}{10000}} \\ & =e^{- \frac{1}{2}} \\ & \approx 0.604 \end{array}$