Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \pi n}{5}}$, where $a_0=1, a_1=$ $3 j, a_2=2 j, a_3=-2 j$ and $a_4=-3 j$. The value of the sum $\sum_{n=0}^4 x[n] \sin \frac{4 \pi n}{5}$ is
- $-10$
- $10$
- $-2$
- $2$