Q: How do I back up my iPhone when I get the message that the last backup could not be completed?

Hello, Maitri4everyone

Thank you for visiting Apple Support Communities.  

I understand that you are unable to backup your iPhone 5s.  I am not sure how you are attempting to backup your device, so I will include the troubleshooting articles that cover both scenarios.  

If you can't make an iTunes backup of your iPhone, iPad, or iPod touch

Get help backing up your device in iCloud

-Jason H.