Q: Hhhh"No backups available" is what my new iPhone 6 is stating while setting it up.

Hi, Jeni78.  

Thank you for visiting Apple Support Communities.  

I understand that you are unable to restore from an iCloud backup of your iPhone 5 on your new iPhone 6.  As it sounds like you have already been through the steps in the first article below, let's start with making sure that the Apple ID being used for the iPhone 6 is the same one being used on your iPhone 5.  I would also recommend going through the remainder of the troubleshooting steps in the second article below.  

If restoring from an iTunes or iCloud backup requires a newer version of iOS

If you need help restoring your device from an iCloud backup

Cheers