Higher frequency bands (>6 GHz) look promising to meet the proposed 5G data rates, given the large amount of available spectrum in these bands. However, a rigorous understanding of some fundamental tradeoffs like network densification, sectorization, and bandwidths has only begun to be investigated at millimeter wave (mmW) bands. In this work, we investigate the coverage and rate performance of cellular networks with sectorized access points (APs) operating at high frequency bands, using tools of stochastic geometry. We observe that sectorizing the APs can significantly improve the data rates and thus can be used in conjunction with network densification, in order to achieve the 5G data rate requirements. However, the increased data rates come at the expense of increased interference in the network. We investigate the interference effects on a typical moderate (200 MHz) bandwidth network at 28 GHz and a high (2 GHz) bandwidth network at 72 GHz carrier frequency, with 4 sector APs and validate the trends observed with the help of detailed system-level simulations using METIS-like scenarios.