http://www.mhhe.com/physsci/astronomy/uspeak/sept_00_uspeak.mhtml
That is the good news. The bad news is disaster could be waiting for us quite a bit sooner than five billion years. The Sun is not constant now and it never has been. Even though our star seems to be in its comfortable middle age it is, in fact, slowly heating up. Every ton of Hydrogen gas that gets converted into Helium forces the Sun to contract just a little bit and that raises its temperature just a bit. In the next 1.1 billion years the amount of energy the Earth will get from the Sun (which is directly related to the Sun's temperature) will increase by almost 10%. That may not seem like much to you, but to a delicately balanced planet's climate far less then 10% can mean the difference between life and death. When scientists examine computer models for a future climate under the revved up Sun they see a Greenhouse effect gone wild. The polar ice caps will be history, and much of the fertile land will be flooded. As the Sun's output continues to increase so much water is evaporated into the atmosphere that even the stratosphere gets wet. Sunlight can then break apart the water molecules allowing the hydrogen atoms to escape into space. No more water, no more life. The world as we know it will have ended.
