Was the entire territory of the former Roman Empire under the rule of barbarians?

We are talking about the events of the 5th century, only the Western Roman Empire was under the rule of the barbarians. In the 5th century, they drove the Romans from the island of Great Britain, the Angles and Saxons invaded there. France was invaded by the Franks and Burgundians, the German provinces were invaded by the Goths, Huns and Alemanni, and later by the Lombards. Vandals invaded North Africa and from there into Italy, the Visigoths took hold on the Iberian Peninsula.

The barbarians failed to conquer the Eastern Roman Empire, in the Balkans, partly in Egypt and the Middle East. In the middle of the 6th century, the Byzantines managed to recapture part of the barbarian kingdoms in North Africa, southern Spain and Italy.