As shown in the picture above, for low pass filter with cut-off frequency, fc = 1 kHz and 5kHz the quality of the waveform varies. Why will the frequency affect the quality of the waveform??

 

I would expect that if you increase the corner frequency of the output filter, you allow more of the high frequency carrier frequency to appear at the output, hence why the output is distorted.

 

The required cutoff frequency is usually determined by the frequency of the Class D PWM frequency.
What is that in your amp?
Is it a subwoofer amp?