In recent years, the fifth-generation (5G) new radio (NR) signals have emerged as a promising supplementary resource for urban navigation. However, a major challenge in utilizing 5G signals lies in their vulnerability to non-line-of-sight (NLoS) propagation effects, which are especially prevalent in urban street canyons. This paper applies the direct position estimation (DPE) method to 5G cellular signals to mitigate the NLoS bias as well as the multipath effects, thereby enabling precise localization in urbanized environments. The feasibility of applying the DPE method to NR positioning is analyzed, followed by a discussion of the tapped delay line (TDL) channel propagation model provided by the 3rd Generation Partnership Project (3GPP). The positioning performance is then evaluated through large-scale system-level simulations. The simulation results demonstrate that 5G DPE achieves satisfactory positioning accuracy in a 10 dB noisy channel, with an overall root mean square error (RMSE) constrained within 6 m. In addition, 5G DPE outperforms the observed time difference of arrival (OTDoA) method by 95.24% in terms of positioning accuracy in an NLoS-dominated propagation environment.