Find $X(j\omega)$ after sampling of $2\cos(2000\pi t)+\sin(5000\pi t)$ at 5 kHz sampling rate
Look at your signal and figure out what sampling rate you need to avoid aliasing. In this case, you are sampling at twice the maximum frequency component so you should not expect aliasing, but you work leads to aliasing components showing up at plus/minus $\frac{3\pi}{5}$. 

Remember that the DTFT is periodic with period $2\pi$, and try re-working the problem.