Wow, my Android OS used 1.75GB in 5 days
Phones always use more data than normal in the first day or so, particularly if you didn't connect it to wifi while it was being set up.

Things that happen in the first day will be checking for (and downloading and installing) OS updates (which can be large), downloading and installing new apps (some of which could be large), syncing data down from the cloud to apps for the first time, syncing data and apps down from backed up Android data to your device.

You might also want to see these previous questions for more info:


How to monitor the amount of data traffic?
Minimizing data usage for users with data caps