This lenovo Vibe K5 update issue occurs due to permission issue. Here are steps to update the Lenovo Vibe K5.
1. Go to settings > System update.
2. Here you have to choose "Download" of system update option.
3. Apply the update.
4. During the update it'll thrown an error.
5. In the bunch of options given at the boot prompt, Here if you are getting the carrier switch error.
6. Stop the update and revert back.
At this point you have to switch the device to the PC.
7. Download the Lenovo smart assistant.
8. Make sure you have enabled the "USB Debugging" option in your phone.
9. During connection with Lenovo assistant it'll ask for ADB permission.
10. Choose Ok and proceed for PC to Phone connection through Smart Assistant.
11. You can find the Update ROM option.
12. Click on "Update ROM" button.
13. It'll download the ROM.
14. During the update patching it'll fail.
15. In this step, you have to find the Lenovo directory on PC and navigate to plugin and update folder.
16. Copy the update.zip file to another location in your hard drive.
17. Extract this zip folder.
18. Get system.zip from this extracted file.
19. Copy the system.zip in your phone memory card.
20. Remove the PC to Phone connection.
21. Shutdown the phone .
22. Get into Stop recovery mode.
23. Browse with volume keys.
24. Choose apply update from memory card.
25. The patch will start updating.
26. Once patched, the update will reboot.
27. System will take you to the phone home screen.
This should update your Lenovo Vibe K5. There are plenty of Youtube tutorials that can point you to visual instructions for this sort of error for updates.