When you purchase an Xbox 360 with a Hard Drive, which is not the cheapest one, it does come with 1 Free month of Xbox Live Gold. There are two types of Xbox Live service, Silver and Gold. Gold allows you to visit the Xbox Marketplace and play multiplayer as while Silver only allows visitation to the Marketplace.
No, it after you succesfully complete the campaign it wont be anywhere near 5 GB, seeing as how thats almost half of the Xbox's Memory in the first place.
As a final note for the Xbox live, simply buy and make an Xbox Live Gold Account which costs 50$ a year. (Not expensive at all)