Unable to complete first backup to iCloud due to lack of space
I also recently noticed that the backup "choose data to back up" section doesn't show up in iOS 11 unless you have an existing backup to select first, since the UI is tucked into the screen when you select a backup for a phone.

If you're willing to go forgo the 99 cent subscription fee for a month, you could increase your storage for iCloud, make a backup, see if you can refine the backup to fit back into the 5GB limit, make a new backup, and then bring your storage plan back down.

I did the first few steps myself, and the backup refinement options do appear in the new backup. I've just been too lazy to followup and actually trim my backup to downgrade my storage plan.

Alternatively, you could go into Settings > General > iPhone Storage, and see if you've got some easy targets using a lot of Documents &amp; Data storage to delete to bring down the size of the backup. Only Documents &amp; Data matters for third party apps, since the apps themselves are not backed up, only the app data (documents &amp; data) is backed up. Also iOS itself is not backed up, only the settings and user data within.