Backups are disabled in iOS 8 beta 5. You need to wait to install the GM and then backup most likely.
Backups may be disabled in Beta 5 if that's what you have.
Apparently it was in the release notes for B5. Backup services disabled.
Odd.. I am pretty sure I was able to backup my Beta 5 just fine.
I tried it multiple times from my MBA and kept receiving an error saying the iPhone could not be backed up because it had been disconnected from iTunes. At first I thought I had a faulty cable, but later learned that backup services had been disabled in B5.
From the release notes:
Known Issues
Encrypted backups to iTunes fail.
iOS 7 iCloud backups restored to an iOS 8 beta device may not properly restore photos.
I tried it on my W7 desktop and couldn't even get it to recognize my iPhone.
I can confirm backups work on beta 5. But GM should be out tomorrow anyways.
In the release notes it says that encrypted backups are unsupported. Just because some people are having problems with backing up (myself included) doesn't mean it is impossible.
From the beta 5 release notes:
"Known Issues
Encrypted backups to iTunes fail."