iTunes and iPhone report different available storage

For my iPhone 5, with iOS 8.4, the phone reports usage of 53.3 GB Used and only 2.2 GB Available, but iTunes shows 48.07 GB Free for this device. Adding up the items listed under Manage Storage on the phone gives a total of about 6.5GB, so iTunes seem to have it right. But the phone acts like it is out of memory.

Responses to other questions I've found here suggested things like turning off iCloud backup, and resetting the phone, but those suggestions did not make a differences. How do I get the iPhone to make use of memory that should be free?

Thanks,

Ted