Simply quit the iTunes software, and launch it again.
If your iTunes software is not up to date, it can cause various issues, including many errors during restore or update of your iPhone. That is why you should download and install the latest version.
Press and hold the sleep/wake button and slide to turn off your iPhone 5c, and then turn it on. Try to sync your device with iTunes again.
The computer can have some glitches, and after the restart, those glitches are gone. Maybe this solution is what you have been looking for.
Back up your files to iCloud. Once you do that, navigate to Settings, tap on General, tap on Reset, and choose Erase all Content and Settings. Usually, this will be over in a few minutes, and once it is, set up your iPhone 5c as a new device.