Double check that you don't have any in "All Mail" that are unread. If you've archived any emails rather than deleting them before reading them, it'll still show the unread count, but you won't see them in your inbox.
You can check the All Mail folder, swipe the menu out from the left. On my Note 4, All mail is already on the list, but you may have to scroll down just a little to see it.
Mine did this in the first couple days of having the phone. I tried clearing cash, deleting and re installing, force closing etc....just restart your phone and it should go away. that was a suggestion i had on here and it worked...wish i would have done that before everything else i did.