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The internet-of-things (IoT) environment connects different intelligent devices together and enables seamless data communication between the connected devices. Connected vehicles (CVs) are one of the primary example of the IoT, and the efficient, reliable, and safe operation of CVs demands a reliable wireless communication system, which can ensure high throughput and low communication latency. The 5G millimeter wave (5G mmWave) wireless communication network offers such benefits, which can be the enabler of CV applications, especially for dense urban areas with high number of CVs. In this study, we present a simulation-based evaluation framework of end-to-end 5G mmWave communication for CV applications. In addition, we compare the 5G mmWave with the Dedicated Short Range Communication (DSRC) technology for a CV application. The simulation framework is developed using two simulators, a network simulator and a traffic simulator. In order to develop the framework in this study, we have used Network Simulator 3 (ns-3) and SUMO, an open-source microscopic roadway traffic simulator. We have used end-to-end latency, packet loss and throughput as the performance evaluation metrics. We have found that for dense urban areas, 5G mmWave can achieve higher throughput, lower latency and lower data loss compared to DSRC. 5G mmWave can support CV applications with high throughput requirement on the downlink data flow. Through further investigation, we have found that the performance of 5G mmWave is significantly impacted by the penetration level of CVs, maximum CV speed, and CV application requirements.