Providing a consistent data rate to users with a highly dynamic activity in a cellular network is a very important feature of 5G. This will lead to increased user satisfaction with services such as video-streaming, online gaming, etc. Knowing that resources are constrained, operators must limit the number of users in the cell, so that admitted users do not experience performance deterioration. In this paper, we consider the problem of admission control for consistent users in 5G cellular systems. We consider two types of users in terms of their rate distributions: 1) homogeneous users, and 2) heterogeneous users. For each user type, we perform the analysis for two scenarios: constant number of users, and random number of users. The analysis is followed by realistic simulations to show that our models can provide satisfactory results in realistic scenarios as well. We also show that the number of admitted users can be significantly increased (up to 3 ×) by allowing a slight deterioration in the QoS.