I'm assuming that the computer in your room is the one you're trying to put Linux onto, and it has the cat5 plugged into it. Firstly, what is the other end of this plugged into? If it's a router, and DHCP is enabled, then it should be easy to select DHCP in the Linux things however it's done. If it's another Windows machine then you'll want to set up Internet Connection Sharing first, and then it's the same as DHCP on the Linux box I think.