The Great Breakout was a period in history, around the year 5000, in which humanity continued to spread out to the stars. This also meant the solar system became busier as large numbers of frontiersmen and pioneers became concentrated in the asteroid belt while waiting to spread out in the galaxy.
The Fourth Doctor noted that the spread of humanity at this time was like a tidal wave or a disease. He added that when humans got together in large numbers, other lifeforms sometimes suffered. (TV: The Invisible Enemy)
This event took place almost nine hundred years after the Revolution of the Ood, at which time the Second Great and Bountiful Human Empire was in control of three galaxies. (TV: Planet of the Ood) Notably, around the same time, Earth was suffering from an Ice Age, a technological cul-de-sac, World War VI, and Magnus Greel's tyranny. (TV: The Talons of Weng-Chiang)