The correct answer is D. 20 kHz.
According to the sampling theorem, the sampling frequency must be greater than twice the maximum frequency of the signal to be sampled. In this case, the maximum frequency of the signal is 5 kHz, so the sampling frequency must be greater than 10 kHz. Therefore, the sampling frequencies of 5 kHz, 12 kHz, and 15 kHz are all valid. However, the sampling frequency of 20 kHz is not valid, because it is not greater than twice the maximum frequency of the signal.
Here is a more detailed explanation of the sampling theorem:
The sampling theorem states that if a band-limited signal is sampled at a rate greater than twice its highest frequency component, then the original signal can be perfectly reconstructed from the samples. This is because the samples contain all of the information about the original signal, up to the Nyquist frequency, which is half the sampling rate.
In this case, the maximum frequency of the signal is 5 kHz. Therefore, the Nyquist frequency is 10 kHz. This means that the sampling frequency must be greater than 10 kHz in order to perfectly reconstruct the original signal. The sampling frequencies of 5 kHz, 12 kHz, and 15 kHz are all greater than 10 kHz, so they are all valid sampling frequencies. However, the sampling frequency of 20 kHz is not greater than 10 kHz, so it is not a valid sampling frequency.