High data usage on iPhone 5?

I'm with Telstra, on a $130/month plan, I get 4.5GB of data a month, which I assumed would be plenty, as when I had an iPhone 4 I used roughly 3GB/month. But, I get messages within the first three days of my month saying I've used all of it. I'm not even using it that much, I check social networking sites every few hours, and then exit out of the app (by double clicking the home button and exiting the app completely) I also have LTE turned off, as well as automatic updates. I don't know where my internet is going, because I can't even use 4.5GB on my computer in a few days let alone using that much on my phone. Anyone have the same issue/any ideas?

Added (1). The only apps that use internet that I have are Facebook, Twitter, Instagram and Snapchat. And I only use them a few times a day before exiting them completely, I don't sit on the app all day.

Do you have many apps that use the Internet a lot eg. Viber, Skype, absolute radio. I have those apps on my iPhone 4 and they use 4.8 GB alone