The paper proposes a novel cell sleeping mechanism for enhancing network energy-efficiency and to combat dynamic downlink interferences linked with mobile Small Cells (mSCs) in a 5G Heterogeneous Cellular Network (HetCN). The proposed Dynamic Mobile Cell Sleeping Mechanism (DMCSM) allows deployed vehicle-mounted mSCs to dynamically go into sleep based on the calculated distances of users from its serving mSCs BS. With this mechanism, vehicular mSCs during mobility dynamically calculate their distances with the Macrocell (MC) users. The mSCs go into sleep or get deactivated for a while based on the calculated distance and the cell radius defined for mSCs. The mSCs will get active and starts to provide services to the users that are found within their coverage radius. The setup 5G HetCN is investigated with a MC superimpose with fixed SCs (fSCs) and mobile SCs (mSCs). The proficiency of DMCSM is investigated with the exploitation of existing sub 6 GHz groups at MCs and the millimeter wave (mmWave) spectrums at deployed fSCs and mSCs. The network downlink performance metrics: user throughput, sumrate, energy-efficiency, and outage probability, have been explored. The work also depicts a comparison of the proposed DMCSM mechanism with the author's previously proposed ICI mitigation techniques.