The Great Breakout was a period in history, around the year 5000, in which humanity continued to spread out to the stars, long following the initial Break-out of the late 21st century. 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) The Ninth Doctor told Rose Tyler that, by the 51st century, humanity would have spread out across "half the galaxy". (TV: The Doctor Dances)
It was during this period when colonies were severing ties with Earth Central that science was no longer something enjoyed by most people and astrology again had considerable importance, recalling the time the former "Age of Reason", from Earth, and making room for what would be the neo-astrology, developed mainly after the contributions of the researcher and astrologer Kasterborus. (PROSE: Introduction and links)
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) as well as their continued involvement in the Great War against the Daleks which began in 4000. (PROSE: The Evil of the Daleks)
Aftermath and legacy
The Fourth Doctor was aware that the time of the Great Breakout preceded the Mordee expedition, the human survey team from which the Tesh and the Sevateem were descended. He revealed this to his companion, Leela of the Sevateem. (TV: The Invisible Enemy, The Face of Evil)