From the Western European perspective, the 5th Century saw the fall of Rome and the end of its empire in the classical form, and the start of the formal transition from the classical period to the middle ages (through, it must be said, the Dark Ages, which may or may not have existed).
In 410 the city of Rome was sacked by Visigothic barbarians ("barbarians" because they happened not to speak Latin). Over the century waves of different nomadic people swept across Europe from east to west, having been uprooted by the first stirrings of the process that was to lead to the Mongol Empire and to the exploration of the East, in reply.
So, the Jutes, Angles and Saxons found pressure in lower Germany, and migrated to southern England (some argue being invited by Vortigern to repel others of their kind). The Romans had, by then, left, packing their bags around 416CE.
The Frankish people (not all called 'Frank', of course, but enough of them so that, as a whole, they were 'Frank-ish') were displaced east into Roman Gaul, and spread down towards Spain, thus setting the foundations for the later Carolingian rule over most of Western Europe (the forerunner of today's EU). Thus Clovis I became King of the Franks in c.481, and in 507 was to expel the Visigoths into Spain and secure Gaul for Frankish-kind.
As things became more difficult in Rome (the city was sacked by the prototype Vandals in 455CE), the Imperial troops and governors in the provinces were either withdrawn, or they "went colonial" and settled in their provinces as petty kings and warlords. The last Roman Emperor was displaced in 476 and although the Byzantine Justinian was to attempt to reoccupy Italy, the Western Empire was dead.
It was also at about this time that the Futhark runic alphabet was brought into general use across Europe (by those who wrote runes), that a heavier plough was developed, allowing the breaking of previously untillable land, that metal horseshoes were made more widely available, and that Christian missionaries reached the farthest limits of then-known Europe -- Ireland.