Simultaneous localization and mapping (SLAM) is a key technology that provides user equipment (UE) tracking and environment mapping services, enabling the deep integration of sensing and communication. The millimeter-wave (mmWave) communication, with its larger bandwidths and antenna arrays, inherently facilitates more accurate delay and angle measurements than sub-6 GHz communication, thereby providing opportunities for SLAM. However, none of the existing works have realized the SLAM function under the 5G New Radio (NR) standard due to specification and hardware constraints. In this study, we investigate how 5G mmWave communication systems can achieve situational awareness without changing the transceiver architecture and 5G NR standard. We implement 28 GHz mmWave transceivers that deploy OFDM-based 5G NR waveform with 160 MHz channel bandwidth, and we realize beam management following the 5G NR. Furthermore, we develop an efficient successive cancellation-based angle extraction approach to obtain angles of arrival and departure from the reference signal received power measurements. On the basis of angle measurements, we propose an angle-only SLAM algorithm to track UE and map features in the radio environment. Thorough experiments and ray tracing-based computer simulations verify that the proposed angle-based SLAM can achieve sub-meter level localization and mapping accuracy with a single base station and without the requirement of strict time synchronization. Our experiments also reveal many propagation properties critical to the success of SLAM in 5G mmWave communication systems.