Complex sentence: The plays were most popular in Europe during the 15th and 16th century;; having grown out of the religiously based mystery plays of the Middle Ages, they represented a shift towards a more secular base for European theatre.
Split into simpler sentences: The plays were most popular in Europe during the 15th and 16th century. Having grown out of the religiously based mystery plays of the Middle Ages, they represented a shift towards a more secular base for European theatre.