It's required that the adc input is within -5V and +5V range, else it
That's not quite true.
You should be able to capitalize on the following part of the data sheet specification: -
Input current, continuous (any pin except power supply pins) –10 to +10 mA
Given also that the input range is: -
Analog input voltage GND – 0.3 V to VDD + 0.3 V
You have a good scope to implement a current limit (and therefore voltage limit) by using a series resistor on your input pins. For instance, if the peak voltage at your input could be as high as (say) 8 volts, a current limit resistor of 1 kohm would produce a current into the ADC input of (8-5.3) volts / 1000 ohms = 2.7 mA i.e. significantly below the 10 mA limit.
I'm not saying you do not need an InAmp to get good circuit performance, but you don't necessarily need one for protecting the ADC.