To cover the high demand for wireless data services for different applications in the wireless networks, different frequency bands below 6 GHz and in millimeter-wave (mm-Wave) above 24 GHz are proposed for the fifth generation (5G) of communication. The communication network is supposed to handle, among others, indoor traffic in normal situations as well as during emergencies. The stairway is one of those areas which has less network traffic during normal conditions but increases significantly during emergencies. This paper presents the radio propagation in an indoor stairway environment based on wideband measurements in the line of sight (LOS) at two candidate frequencies for 5G wireless networks, namely, 3.5 GHz and 28 GHz. The path loss, root mean square (RMS) delay spread, K-factor results, and analysis are provided. The close-in free-space reference distance (CI), floating intercept (FI), and the close-in free-space reference distance with frequency weighting (CIF) path loss models are provided. The channel parameters such as the number of clusters, the ray and cluster arrival rates, and the ray and cluster decay factors are also obtained for both frequencies. The findings of the path loss show that the CI, FI, and CIF models fit the measured data well in both frequencies with the path loss exponent identical to the free-space path loss. Based on clustering results, it is found that the cluster decay rates are identical at both bands. The results from this and previous measurements indicate that at least one access point is required for every two sections of the stairway to support good coverage along the stairwell area in 5G wireless networks. Moreover, for 5G systems utilizing mm-Wave frequency bands, one access point for each stair section might be necessary for increased reliability of the 5G network in stairwell environments.