There has been vast research going on in multiple domains of 5G communication and also the effects of 5G on health [1]. This manuscript proposes the implementation of antenna proposed for 5G cellular communication and measuring the Specific Absorption Rare (SAR) in order to address whether the antennas being proposed for 5G communication could commercially be used according to criteria by Frequency Communication Commission (FCC). In this paper, a compact size dual bands square patch antenna has been modeled on two different software platforms High Frequency System Simulator (HFSS) & Computer Simulation Technology (CST) for 5G cellular communication. The proposed antenna has a compact structure of 19×19×0.787mm3 including the ground plane which operates at 10.137 GHz and 28 GHz. The antenna has been designed on Rogers5880 substrate with a thickness of 0.787mm. The proposed design provides a gain of 5.61 dB at 10.176 GHz and 9.485 dB at 28.39 GHz using CST software and a gain of 7.324dB at 10.12 GHz and 9.573 dB at 29.6GHz by using HFSS software. The SAR is calculated at the operating frequency of 10.176 by averaging over a specific volume (typically a 1gram or 10gram area) and the maximum values as 0.8W/kg on 1 gram of tissues and 0.2W/kg on 10 grams of tissues have been calculated. Similarly, at the frequency of 28.39GHz, the maximum values of 1.4w/kg on 1 gram of tissues and 0.3w/kg on 10 grams of tissues are obtained.