This paper presents the comprehensive design and evaluation of a novel large-scale millimetre-wave (mm-wave) two-dimensional (2-D) 64-element antenna array, for operation in the 28-GHz frequency band. The primary objective of this work is to study the feasibility of designing a high-performance array based on liquid-crystal polymer (LCP) substrate for the deployment in the fifth generation (5G) wireless communication networks and infrastructures. The planar 5G array has presented an impedance bandwidth of 400-MHz, with a peak gain of 23.2 dBi at 27.7-GHz. Moreover, the operation of the mm-wave antenna array has been analysed and validated through a set of high-resolution full-wave electromagnetic (EM) simulations, conducted based on the time-domain finite integration technique (FIT). The proposed 28-GHz 2-D antenna array is a high-performance subsystem in order to be potentially employed in the next-generation 5G communications.