It depends on what material you´re measuring. For example, ion-exchange membranes are known to have generally non-Ohmic current-voltage characteristics (due to the current-induced concentration polarization). With such materials by increasing the amplitude you could already get beyond the linear response range. However, more specifically I don´t think that by increasing from 5 mV to 10 mV you would get it really pronounced. The answer depends also on the measurement scheme (number of electrodes) the distance between the indicator electrodes and material surface.

If There os no change in EIS measurement values That means electrchemical system is linear.

Depending on the electrode system you are dealing on, the Nyquist plot and corresponding values can change; look at books on EIS to understand.