My iPhone 5S can't verify iCloud but it can log into the iTunes store. I don't know what has happened. Please help me understand how this happened and what I can do to fix the problem.
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Did you try using this ID and password on any other device or sign into your iCloud from any computer. Also you can go to your iTunes connect your phone to the computer go to the top menu and check how many computers or devices you have authorized on that ID as far as I know you can only authorize five devices on One Apple ID if nothing works out for you then you should back up your phone with computer using iTunes latest version of iTunes and then remove everything on your phone I mean reset or restore your phone then set it up all over as a new phone then restore it from the back up you just made you should be able to get everything back that you had on your phone and your problem should be solved.