In urban environments, cellular network-based positioning of user equipment (UE) is a challenging task, especially in frequently occurring non-line-of-sight (NLOS) conditions. This paper investigates the use of two machine learning methods – neural networks and random forests – to estimate the position of UE in NLOS using best received reference signal beam power measurements. We evaluated the suggested positioning methods using data collected from a fifth-generation cellular network (5G) testbed provided by Ericsson. A statistical test to detect NLOS conditions with a probability of detection that is close to 90% is suggested. We show that knowledge of the antenna are crucial for accurate position estimation. In addition, our results show that even with a limited set of training data and one 5G transmission point, it is possible to position UE within 10 meters with 80% accuracy.