The high demand for wireless wideband services has led to evolving of a new mobile network standard, which is known as ‘5G’. For 5G to meet the essentials in terms of bandwidth, the industry should leverage the mm-Wave band (24-300 GHz). Further, miniaturized antennas that operate in multiple frequency bands are required for future space-constrained devices. In this manuscript, a compact dual-band circular microstrip antenna which has a square ring defected ground structure (SR-DGS) is investigated for 5G mobile systems. The design is accomplished using Ansys-HFSS 2021R1. The Rogers RT/duroid (5880) substrate, which has a permittivity of 2.2, a tangent loss of 0.0009, and a thickness of 1.575 mm, is used as a dielectric material. The antenna has physical dimensions of 5x4x1.575 mm3 with an electrical size of 0.458λ₀ x0.366λ₀ x0.144λ₀ ; λ₀ represents the wavelength in free space at 27.50 GHz. Impedance bandwidths of 1.34 GHz (27.50 GHz-28.84 GHz) and 2.26 GHz (37.74 GHz-40 GHz) are achieved at the 28 GHz and 38 GHz bands, respectively. The antenna resonates at 28.1875 GHz and 38.5625 GHz with respective gains of 7.2 dB and 7.65 dB. The proposed antenna is a promising candidate for 5G communications due to its miniaturized size.