The radiation hardness of Semi-Insulating (SI) GaAs detectors against 5 MeV electrons is investigated in this paper. The influence of two parameters, the accumulative absorbed dose (from 1 to 120 kGy) and the applied dose rate (20, 40 or 80 kGy/h), on detector spectrometric properties was studied. The electron irradiation has negatively affected the detector CCE (Charge Collection Efficiency). Un-irradiated detectors exhibited the CCE of 79% at maximum operating reverse voltage of 300 V and reached the maximum CCE of 51% at 200 V after irradiation by a dose of 120 kGy. Relative energy resolution was also affected by electron irradiation. Its global degradation was observed in the range of doses from 24 up to 120 kGy, where an increase from 19% up to 39% at 200 V reverse voltage was noticed. On the other hand, a global increase of detection efficiency with dose, by about 30% at 120 kGy, was observed with all samples. We did not observe any significant influence of chosen dose rates applied during irradiation on investigated spectrometric properties of detectors.