In a new football league there are five teams: Allesley, Bannerbrook, Canley, Dunsmore and Earlsdon. Over the course of 10 weeks, each team must play every other team twice (once home and once away). There will be two games each week, with one team getting a rest. It is your job to organise the fixtures.

Is it possible to organise the fixtures so that each team alternates between home and away games?

If it is, find an example fixture list; if it is not, why not?