This paper proposes a theoretical analysis for evaluating the statistical distribution of the bit error rate (BER) for a millimeter-wave uplink communication involving a mobile terminal (MT) and a base station (BS). The analysis is focused on the line-of-sight scenario, whose investigation provides useful insights on the maximum performance achievable by forthcoming fifth-generation (5G) wireless networks. The developed model accounts for path-loss attenuation and directional antenna gains assuming a noise-limited operating regime. The location of the MTs around the 5G BS is described by a Poisson point process, while the statistic of the BER is estimated by considering the phase-shift keying (PSK) and the quadrature amplitude modulation (QAM) schemes. The analytical results are finally exploited to discuss the dependence of the error rate from the cell radius and the modulation order in a mmWave context.