UMTS:
The delay from transitioning to DCH to FACH is governed by a timer called T1, and in this case the network has configured it to be 5 seconds. Whatever the value is, it is a compromise between device battery consumption and managing the signalling load between the network elements.
For mobile applications that exchange small packets periodically but infrequently a long timer causes the device to remain in high power state for many additional and unnecessary seconds, draining battery.
Prior to 3GPP Release 8 this issue was addressed by device manufacturers so that instead of waiting for the network initiated transition to FACH, the device would send a signalling connection release indication (SCRI) after it was done sending and receiving data. This would place the device in idle mode, the lowest power consumption state.
However, this solution had an downfall: the SCRI would cause unnecessary signalling load between the network elements when the RAB was being released and set up again frequently.
This was addressed in Release 8 so that a specific cause value (UE requested PS data session end) in SCRI explicitly states to the network that the device is done sending and receiving data. This allows the network to distinguish between different reasons for releasing the connection, and if it is happening too frequently, it could deny the request to release the connection and avoid signalling load.
See Fast Dormancy Best Practices by GSMA for more info.
LTE:
LTE is simpler as there are only two RRC states, connected and idle. The timers are still controlled by the network, but remaining in RRC connected state in LTE is not as harmful to the UE as discontinuous reception (DRX) helps to keep the power consumption lower. Also, transitioning between the two states does not cause as much signalling load in LTE, as it was a goal of the design.