iCloud won't let me back up, even with full 5.0 GB available I have the new iPhone 5S with 64 GB, which I got so I wouldn't have to be always deleting stuff. 

Now I've tried deleting both of the 2 backups that were on my phone iCloud - 2.4 GB &amp;  2.6 GB --- to clear out space. It was saying the next back up would require 3.1 GB.

When I go to Storage &gt; Manage Storage in the Settings app, the only option that shows up is "Change Storage Plan." There is no option to back up. I don't want to have to buy storage. If it was going to need 3.1 GB, why is 5.0 GB of free iCloud space not enough to perform a backup? I did backup to my computer using iTunes before doing the delete of the iCloud backups, but I'd like to back up to iCloud too.
You're supposed to go 
Settings -> iCloud -> Backup -> Turn it on