Base stations (BSs) sleeping strategy has been widely analyzed nowadays to save energy in 5G cellular networks. 5G cellular networks are meant to deliver a higher data speed rate, ultra-low latency, more reliability, massive network capacity, more availability, and a more uniform user experience. In 5G cellular networks, BSs consume more power which is about 4 times that of 4G. To reduce average power consumption and save power in 5G, we have modelled the 5G BSs sleeping mechanism as an M/G/1 queue with two types of vacations (two different sleep modes), idle period (close-down), and set-up periods. Based on the traffic load, the BSs adjust their transmitting power in the active state, idle state (close down state), sleep mode 1 (type 1 vacation), sleep mode 2 (type 2 vacation) and set-up state. The length of sleep mode 1 is smaller than the length of sleep mode 2. Sleep mode 1 consists of a maximum M sleeps. When the BSs are in sleep mode or shut off, they will experience a state delay. To overcome this delay, it is necessary to optimize sleep in sleep mode 1 considering a small amount of set-up time. To optimize the maximum sleeps in sleep mode 1, the tradeoff between power consumption/power-saving and throughput is shown. Finally, the trade-off between power consumption and saving is presented to get the energy efficiency from 5G BSs. Without finding the energy efficiency i.e., optimal power consumption and power saving in 5G BSs, it will not be possible to say how much the model is effective for use in 5G BSs.