Re: why doesn't my 5s auto backup
After you've turned on iCloud Backup, iCloud can automatically back up your device each day. iCloud makes these daily automatic backups only if:
Your device is connected to a power source.
Your device is connected to a Wi-Fi network.
Your device's screen is locked.
You have enough available space in iCloud for the backup.
Source:
https://support.apple.com/en-us/HT203977