A key point of Fifth Generation (5G) wireless networking will be the exploitation of higher frequency bands in the millimeter wave (mm-Wave) spectrum to provide unprecedented data rates to mobile users. In such a perspective, the PHYsical (PHY) layer design priorities should be reconsidered. In this paper, we investigate Constant-Envelope Multicarrier (CE-MC) waveforms for future adoption in mm-Wave 5G transmissions, namely: Constant-Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM) and Constant-Envelope Single-Carrier OFDM (CE-SC-OFDM). These waveforms are obtained by imposing a nonlinear phase modulation to a real-valued OFDM and SC-OFDM signal, respectively. Thanks to their 0dB Peak-to-Average-Power Ratio, such unconventional signaling formats are insensitive to nonlinear distortions and allow to exploit the flexibility of conventional multicarrier systems together with augmented resilience against multipath fading and phase noise. CE-OFDM and CE-SC-OFDM have been assessed by means of computer simulations in a short-range mm-Wave 5G scenario, i.e., downlink transmission in outdoor picocells. Simulation results demonstrate that CE multicarrier waveforms enhance robustness and increase coverage and capacity in the proposed scenario, as compared to conventional OFDM and SC-OFDM counterparts.