5G communication systems provide an end-to-end wireless connection to billions of users and devices across the globe. The behavior of the radio propagation channel plays a significant role in the quality of signals received during radio communication. A central parameter used in characterizing this channel is the Path Loss Exponent (PLE). Several works that have estimated and analyzed the PLE mainly considered the effect of distance and carrier frequency at the microwave band. However, the effect of base station antenna height and channel bandwidth on the PLE for 5G networks has not been adequately considered. Hence, this work investigates the effect of base station antenna height and channel bandwidth on the PLE at the 5G millimeter wave frequency band, considering 24, 38, and 66 GHz. The licensed EDX Signal Pro software ® with Cirrus high-resolution global terrain and clutter database was used to model, simulate, and analyze the path loss exponent for Kano City, Nigeria. Results showed that an increase in base station height or channel bandwidth for the tested frequencies leads to a significant reduction in the path loss exponent. This study can be utilized by network planning engineers and the wireless research community to improve further network implementation and optimization toward understanding signal propagation behavior in 5G networks and beyond.