This term is usually reserved for the 5th and 6th centuries. Re-enactors who re-create the next period of history - 7th to 11th centuries - often refer to this as Early medieval. The 12th to 14th are High medieval.
A medieval reenactment is a form of historical reenactment that focuses on re-enacting European history in the period from the fall of Rome to about the end of the 15th century. The 2nd is the Middle Ages.