The fleet management of mobile working machines with the help of connectivity can increase safety and productivity. Although in our previous study, we proposed a solution to use IEEE 802.11p to achieve the fleet management of construction machines, the shortcoming of WIFI may limit the usage of this technology in some cases. Alternatively, the fifth-generation mobile networks (5G) have shown great potential to solve the problems. Thus, as the worlds first academic paper investigating 5G and construction machines cooperation, we demonstrated the scenarios where 5G can have a significant effect on the construction machines industry. Also, based on the simulation we made in $ns-3$, we compared the performance of 4G and 5G for the most relevant construction machines scenarios. Last but not least, we showed the feasibility of remote-control and self-working construction machines with the help of 5G.