The current trend has seen the data capacity and traffic density increase due to the increased demand for multimedia services. Since this cannot be handled successfully by the current 4G networks, there is a need to integrate the mmWave and the Device-to-Device (D2D) communication 5G technologies to meet this increased demand and traffic density. However, there is the challenge of increased interference between dense D2D users and cellular users if D2D users are allowed to reuse the resources allocated to cellular users. This degrades the performance of the D2D users in terms of achievable data rate and Energy Efficiency (EE). The paper formulates a match theoretic resource allocation scheme to maximize the achievable D2D sum rate. In addition, an EE optimization problem is formulated for D2D users by considering the rate and power constraints. The EE optimization problem is solved by the Lagrangian dual decomposition method. The algorithms were simulated in MATLAB and the results were compared to Hungarian and heuristic optimization algorithms. The results showed that the match theoretic resource allocation is on average 1.82 times better than the Hungarian algorithm. At the same time, the match theoretic resource allocation algorithm increases fairness in resource allocation as it maintains a higher sum rate for low and high-density number of users. The proposed EE optimization algorithm improved the D2D performance by 8.2% compared to the heuristic algorithm.