Q: Photo App on iPhone 5 has "syncing" message at bottom.

Hello, dangles8. 

Thank you for visiting Apple Support Communities. 

I would first start with forcing all open applications to close and power cycle the device.  Test opening the Photo App on your device to see if they load.  If the issue persists, see the second article below. 

iOS: Force an app to close

http://support.apple.com/kb/ht5137

iTunes: Unable to sync photos

http://support.apple.com/kb/TS3697

Cheers,

Jason H.