Step 1: Charge the phone
The owner didn’t mention she tried to charge the phone after it went dead so this must be the first thing that needs to be done as it could be just a drained battery.
This step would also give us an idea about the integrity of the phone’s hardware. If the charging signs show, like the LED indicator and the charging icon, then the phone must be okay. Just allow it to charge for, at least, ten minutes.
If the device refused to charge, read this: How To Fix Samsung Galaxy S5 Charging Problems [Troubleshooting Guides]
Step 2: Attempt to turn it on after charging
Ten minutes of charging is more than enough to power the phone if the issue was a drained battery. So, attempt to turn it on after a few minutes of charging.
If the phone turns on, continue the observation if it turns off on its own but if not, then read this post instead: How to fix Samsung Galaxy S5 that won’t turn on [Troubleshooting Guide]
Step 3: Wipe the cache partition
Assuming the phone turns on just fine but shuts down on its own, then you must try wiping the cache partition considering the fact that you just updated it to lollipop.
During updates, some caches and data become corrupt and if the new system continues to use them, that’s when conflicts are created. Clear these files so the phone will be forced to create new ones and aren’t obsolete.
Turn off the device.
Press and hold the following three buttons at the same time: Volume Up key, Home key, and Power key.
When the phone vibrates, release the Power key but continue to press and hold the Volume Up key and the Home key.
When the Android System Recovery screen appears, release the Volume Up and Home keys.
Press the Volume Down key to highlight ‘wipe cache partition.’
Press the Power key to select.
When the wipe cache partition is complete, ‘Reboot system now’ is highlighted.
Press the Power key to restart the device.
Step 4: Verify the Power key isn’t stuck
This is optional but also important since the owner said the phone turns on and turns off on its own and then vibrates. She didn’t really say if it goes into a loop or how frequent the phone shuts down but it’s necessary.
Don’t worry, it’s easy to check if the Power key is stuck or not; just press it and if it snaps, then it’s not stuck. Otherwise, try pressing it multiple times to see if you can fix it. If not, then you really need help from a technician.
Step 5: Perform the full hard reset
If the phone turns on and turns off by itself, it’s either the hardware that’s causing it or the firmware. But the owner said the problem started immediately after an update. So, hardware issue is out of the question.
Since you’ve already followed the previous steps to no avail, then it’s time to give the phone a fresh start–reset it. But before you actually do that, make sure you backup all important data and files saved in the phone’s internal storage.
If you have a microSD card mounted, un-mount it as it may be corrupted during the process.
Turn off the device.
Press and hold the following three buttons at the same time: Volume Up key, Home key, and Power key.
When the phone vibrates, release the Power key but continue to press and hold the Volume Up key and the Home key.
When the Android System Recovery screen appears, release the Volume Up and Home keys.
Press the Volume down key several times key to highlight ‘wipe data / factory reset.’
Press Power button to select.
Press the Volume down key until ‘Yes — delete all user data’ is highlighted.
Press Power button to select and start the master reset.
When the master reset is complete, ‘Reboot system now’ is highlighted.
Press the Power key to restart the device.
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