Removing an unwanted sinusoidal signal using FIR filter
A very straightforward-answer, without a lot of calculation:

The magnitude of the frequency response of a filter is the magnitude of its z-Transform on the unit circle. Hence, if your filter should filter out a specific frequency, it needs to have a zero at exactly this frequency in the unit circle.

Considering that $f_s=10kHz$, a full rotation on the unit circle relates to $10kHz$. A sine has frequency components at $f_n$ and $-f_n=f_s-f_n$ (considering the periodicity of the DTFT due to the sampling). Hence, there need to be zeros at 2.5kHz and 7.5kHz, corresponding to 90 and 270 degree on the unit circle. Accordingly, the zeros need to be at $z=\pm j$.