Camera not working on Facetime or Skype on iPhone 5s

Good evening.

I have a brand new iPhone 5s, updated to iOS 7.1.2. There are no restrictions enabled on it.

The camera simply does not work on either Facetime or Skype (latest version), no matter what I tried. Audio is fine, I can hear/see the other person. My contacts have the latest version of iOS/Skype installed.

I should mention that the normal camera app works just fine - I can take photos or record video. However, after a failed Skype/Facetime call, if I try to open the normal camera app and take a photo, it will show the controls over a black screen and it will block. After a reboot it works normally and I can take photos again.

Any ideas would be deeply appreciated. Thanks.