Try to follow Blaze6377 first.
If it doesn't solve your problem.
Here is what I did and it SOLVED! for my iPhone 5:
1. Close iTunes and reopen your iTunes program again.
2. Plug in your iPhone 5 with your computer.
3. Press Power button and Home button together again.
4. This time iTunes will show iPhone 5 will be in recovery mode. Just close the pop up messege in iTunes.
5. My iPhone's screen shows to plug in cable with iTunes. I just remove the cable out from my iPhone instead.
6. Press and hold Power button and Home button together again. It will shows Apple logo first, then disapear, then it shows Apple logo again. At this point, release both buttons.
Under the Apple logo, it will show grey bar (like computer boot up). Just wait and then Voila!. My iPhone came back to normal again.
I did the above processes because I try to avoid from Restore to factory setting.
I hope this help and work with your iPhone as well.
Have a good one! 😉