The Battle of Installation 05 was an engagement between the Covenant forces, including those that fled the Battle for Earth, High Charity, and the Second Fleet of Homogeneous Clarity, and the UNSC-allied forces, including the UNSC In Amber Clad led by Miranda Keyes, and the Fleet of Retribution led by the Arbiter Thel 'Vadam. While the battle began between the Covenant forces that fled Earth with the Prophet of Regret and the In Amber Clad, it quickly became complicated with the arrival of the Prophets of Mercy and Truth, High Charity, and the start of the Great Schism, Truth's plan to replace the Sangheili leadership with Jiralhanae and its subsequent civil war.
John-117, along with a squad of ODSTs, were sent ring-side to kill Regret, and unknown to him, was allowed to succeed by the actions of Truth. Meanwhile, Miranda Keyes, Avery Johnson, and the rest of In Amber Clad attempted to retrieve Installation 05's index in order to prevent the Covenant from firing the Halo. They were successful, though the Jiralhanae forces led by Tartarus stole it from Keyes and took her captive.
Unbeknownst to the UNSC at the time, the Flood had made a presence on Installation 05 for many centuries, and further complicated the battle. The Gravemind, sensing both a threat from the Covenant forces and a potential way to get off the ring, utilized both Master Chief and the Arbiter to remove the threat and infect their ships, including In Amber Clad and High Charity. The Flood was successful in killing the Prophet of Mercy, but Truth managed to escape with the desire to return to Earth and get to the Ark. Though High Charity was lost to the Flood, Truth was still able to get to the Forerunner keyship located on High Charity and escape back to Earth. Master Chief pursued, but Cortana stayed behind in order to ensure the destruction of Installation 05 and High Charity if the Flood outbreak could not be contained.
While Tartarus was able to take control of the Index, the UNSC and Arbiter-allied forces were able to stop him from firing the Halo. Although the activation of the Halo was stopped, Tartarus managed to get all the other Halo installations into standby mode, meaning they could easily be activated from the Ark, Installation 00.
These events are depicted in the video game Halo 2.