A compact-size quad-band (28/45/51/56 GHz) microstrip patch antenna is proposed for the Fifth Generation (5G) mobile handsets. The present paper introduces a new method to reduce the size of a 28-GHz rhombic patch antenna so as to properly operate at the higher frequency bands (45/51/56 GHz) without negative effects on the antenna characteristics at 28 GHz. A novel design is introduced for the quad-band patch antenna to include complicated radiation mechanisms required for multiple-band operation. The proposed (single-element) antenna is constructed as primary and secondary patches which are capacitively coupled and designed to realize impedance matching and to produce appropriate radiation patterns in the four frequency bands. Two-port and four-port MIMO antenna systems that employ the quad-band patch antenna are proposed in the present work for the 5G mobile handsets. Numerical and experimental investigations are achieved to assess the performance of both the single-element antenna and proposed MIMO antenna systems including the return loss at each antenna port and the coupling coefficients between different ports. It is shown that the simulation results agree with the experimental measurements, and both show good performance. The bandwidths achieved around 28, 45, 51, and 56 GHz are about 0.6, 2.0, 1.8, and 1.3 GHz, respectively. The radiation patterns produced when each port is excited alone are shown to be suitable for spatial diversity scheme with high radiation efficiency. It is shown that the envelope correlation coefficient (ECC) and diversity gain (DG) are perfect over the four frequency bands.