Final answer:
The Angles and Saxons, Germanic tribes from modern-day southern Denmark and northern Germany, established rule in Britain during the 5th and 6th centuries.
Step-by-step explanation:
The Germanic tribes that established rule in Britain in the 5th and 6th centuries were known as the Angles and the Saxons. These groups, originally from modern-day southern Denmark and northern Germany, invaded and occupied southern Britain after the Romans left. This period saw the creation of Anglo-Saxon England, a time when Roman culture nearly vanished and the historical record shifted to focus on these Germanic invaders.