Waveshare ADC Board changing analog input range
I need to change the input range of the ADC from 0 to 5V to -2.5V to
  +2.5V. Can this be done by changing ADC registers


The data sheet tells you the maximum working input voltage range for the ADC: -



You are pretty much limited to input voltages between AGND and AVDD - 2 volts with the buffer active and slightly better if the buffer is inactive.

If you have signals that drop below 0 volts then you need to offset them in hardware. An op-amp could work but it depends on what your signals are.