Device-to-device (D2D) communication is considered the most promising technology for 5G networks which enables high speed communication in low latency time. D2D communications allows direct links without using central base stations (BSs). Millimeter wave (mmWave) technology is characterized by short distance directive propagation, and more available spectrum for communication. Integrating D2D communication with mmWave technology significantly enhances the system performance and reaches the demand for high capacity. In mmWave D2D communications 5G underlay networks, multiple cellular users (CUs) and D2D users co-exist. Since D2D pairs can utilize the spectrum assigned to CUs, efficient resource allocation algorithms are required. In this paper, a resource allocation problem in mmWave D2D communications 5G underlay network is investigated. A new resource allocation scheme that allows D2D pairs to share resource blocks (RBs) with cellular users is proposed. The proposed scheme prevents congestion on over a few resource blocks while the rest of resource blocks remain vacant through identifying a set of recommended resource blocks for each D2D pairs. The proposed scheme reduces interference by excluding interferer D2D pairs from resource blocks sharing process for each D2D pairs. The proposed scheme maximizes the spectral efficiency while satisfying minimum QoS requirements. The simulation results show the superiority of the proposed scheme in terms of spectral efficiency and outage capacity.