Anything that has a lot of graphics uses a lot of data. Anything with video uses a huge amount of data. As others have said, the games are going to use your data and fast. One hour of streaming movie uses one GB of data. Watch two and a half full length movies and you have used all of your 5 GB data for the month.
Things like text, email, basic webpage browsing, reading Facebook (without the ads and not playing any video or games) will not use much data at all.
A PC or laptop connected by wifi or wire to a cell data service will use much more data looking at the same webpages than would be used looking at those same pages on a tablet or phone connected to the same data stream. Multiple computers connected at the same time - watch out, the data usage is just flying.
The cell data providers are happy to sell you more GBs if you go over but is it worth it? There are a few cell companies that will sell you a plan with actual truly unlimited data but most that say "unlimited" are not and will either charge you if you go over - which is why you got the letter of warning - or will slow your data connection down to a point where you can't do much more than read email and look at basic websites.
