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Non-orthogonal multiple access (NOMA) plays an important role in achieving high capacity for fifth-generation (5G) networks. Efficient resource allocation is vital for NOMA system performance to maximize the sum rate and energy efficiency. In this context, this paper proposes optimal solutions for user pairing and power allocation to maximize the system sum rate and energy efficiency performance. We identify the power allocation problem as a nonconvex constrained problem for energy efficiency maximization. The closed-form solutions are derived using Karush–Kuhn–Tucker (KKT) conditions for maximizing the system sum rate and the Dinkelbach (DKL) algorithm for maximizing system energy efficiency. Moreover, the Hungarian (HNG) algorithm is utilized for pairing two users with different channel condition circumstances. The results show that with 20 users, the sum rate of the proposed NOMA with optimal power allocation using KKT conditions and HNG (NOMA-PKKT-HNG) is 6.7% higher than that of NOMA with difference of convex programming (NOMA-DC). The energy efficiency with optimal power allocation using DKL and HNG (NOMA-PDKL-HNG) is 66% higher than when using NOMA-DC.