I have data usage charges showing up on my Iphone 5s every day at 5:40am Eastern time. The problem is that my phone is not being used at that time of day and is always connected to WiFi while I am home. The data usage has been very large, from 60mb all the way up to 100mb. I see that others have posted similar concerns so I'm throwing my voice in here saying that this is not our imagination, it is happening and killing out data usage.
Here is a screen grab of my data usage. As you can see, every day at 5:40am, there is a large spike in usage. My phone is not in use at that time:

There must be an explanation and resolution for this.