Summary Recently, academic and industrial research communities are paying more explicit attention to the 5G multiple radio access technology ultra‐dense networks (5G multi‐RAT UDNs) for boosting network capacity, especially in UD urban zones. To this aim, in this paper, we intend to tackle the user association problem in 5G multi‐RAT UDNs. By considering the decoupled uplink/downlink access (DUDA), we divide our user association problem into two distinct subproblems representing, respectively, the uplink and the downlink channels. Next, we formulated each one as a nonlinear optimization problem with binary variables. Then, to solve them, we were restricted by the hard complexity, as well as the hard feasibility of centralized user association schemes. Thus, to resolve our user association problem in a reasonable time and distributed manner, we formulated each subproblem as a many‐to‐one matching game based on matching theory. Next, we provide two fully distributed association algorithms to compute the uplink and downlink stable matching among user equipments (UEs) and base stations (BSs). Simulation results corroborate our theoretical model and show the effectiveness and improvement of our achieved results in terms of the overall network performance, quality of service (QoS), and energy efficiency (EE) of UEs.