Question: What period of time did the Chester Mystery Plays and Medieval theatre become popular?

Context paragraphs:
The Nativity (play): The Nativity was a 58-minute United States television drama with music about the birth of Jesus Christ, presented on the television anthology "Westinghouse Studio One".  Directed by Franklin Schaffner, it is a rare modern network television production of an authentic mystery play, mostly culled from the York and Chester mystery plays of the 14th and 15th centuries in England.  The adaptation was by Andrew Allan.  The presentation, originally telecast live the evening of December 22, 1952 on CBS, has been preserved on kinescope.  It has been issued in several DVD public domain versions.  It can also be seen complete online on Internet Archive.

Chester Mystery Plays: The Chester Mystery Plays is a cycle of mystery plays dating back to at least the early part of the 15th century.

Ophaboom Theatre Company: The Ophaboom Theatre Company, founded in 1991 by Geoff Beale and Howard Gayton, is an English physical theatre company specializing in creating and performing contemporary works in the Italian Commedia dell'Arte tradition.  Drawing on Medieval theatre and the origins of Commedia, Ophaboom set out with the self-stated aim of creating "a popular (and politically topical) style of theatre that would resonate with a modern audience, in the manner of Medieval strolling players."  Although the troupe performs in traditional theatre spaces, they also set up their trestle stage on street corners, in village halls, in bowling alleys and many other less conventional venues, with the stated intention of "bringing theatre to audiences who might not otherwise go to see it."

Medieval theatre: Medieval theatre refers to theatrical performance in the period between the fall of the Western Roman Empire in the 5th century A.D. and the beginning of the Renaissance in approximately the 15th century A.D. Medieval Theatre covers all drama produced in Europe over that thousand-year period and refers to a variety of genres, including liturgical drama, mystery plays, morality plays, farces and masques. Beginning with Hrosvitha of Gandersheim in the 10th century, Medieval drama was for the most part very religious and moral in its themes, staging and traditions.  The most famous examples of Medieval plays are the English cycle dramas, the York Mystery Plays, the Chester Mystery Plays, the Wakefield Mystery Plays and the N-Town Plays, as well as the morality play, "Everyman".  One of the earliest surviving secular plays in English is "The Interlude of the Student and the Girl" (c. 1300).

Morality play: The morality play is a genre of Medieval and early Tudor theatrical entertainment.  In their own time, these plays were known as interludes, a broader term for dramas with or without a moral.  Morality plays are a type of allegory in which the protagonist is met by personifications of various moral attributes who try to prompt him to choose a Godly life over one of evil.  The plays were most popular in Europe during the 15th and 16th centuries.  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.  The earliest known morality play is Hildegard von Bingen's "Ordo Virtutum" (English: "Order of the Virtues") composed c. 1151.  It is the earliest morality play by more than a century, and the only Medieval musical drama to survive with an attribution for both the text and the music.

Mystery play: Mystery plays and miracle plays (they are distinguished as two different forms although the terms are often used interchangeably) are among the earliest formally developed plays in medieval Europe.  Medieval mystery plays focused on the representation of Bible stories in churches as tableaux with accompanying antiphonal song.  They told of subjects such as the Creation, Adam and Eve, the murder of Abel, and the Last Judgement.  Often they were performed together in cycles which could last for days.  The name derives from "mystery" used in its sense of "miracle," but an occasionally quoted derivation is from "ministerium", meaning "craft", and so the 'mysteries' or plays performed by the craft guilds.

Wakefield Mystery Plays: The Wakefield or Towneley Mystery Plays are a series of thirty-two mystery plays based on the Bible most likely performed around the Feast of Corpus Christi probably in the town of Wakefield, England, during the late Middle Ages until 1576.  It is one of only four surviving English mystery play cycles.  Some scholars argue that the Wakefield cycle is not a cycle at all, but a mid-sixteenth-century compilation, formed by a scribe bringing together three separate groups of plays.

Lincoln Mystery Plays: The Lincoln Mystery Plays are modern performances of medieval mystery plays and other productions in Lincoln Cathedral and the surrounding area.

Coventry Mystery Plays: The Coventry Mystery Plays, or Coventry Corpus Christi Pageants, are a cycle of medieval mystery plays from Coventry, West Midlands, England, and are perhaps best known as the source of the "Coventry Carol".  Two plays from the original cycle are extant having been copied from the now lost original manuscript in the early 19th century.  A separate "Ludus Coventriae" once thought to belong to the Coventry cycle of Mystery Plays is now believed to have originated in East Anglia.

York Mystery Plays: The York Mystery Plays, more properly the York Corpus Christi Plays , are a Middle English cycle of 48 mystery plays or pageants covering sacred history from the creation to the Last Judgment.  They were traditionally presented on the feast day of Corpus Christi (a movable feast on the Thursday after Trinity Sunday, between 23 May and 24 June) and were performed in the city of York, from the mid-fourteenth century until their suppression in 1569.  The plays are one of four virtually complete surviving English mystery play cycles, along with the Chester Mystery Plays, the Towneley/Wakefield plays and the N-Town plays.  Two long, composite, and late mystery pageants have survived from the Coventry cycle and there are records and fragments from other similar productions that took place elsewhere.  A manuscript of the plays, probably dating from between 1463 and 1477, is still intact and stored at the British Library.

Supporting paragraphs: Medieval theatre Chester Mystery Plays
Answer: the period between the fall of the Western Roman Empire in the 5th century A.D. and the beginning of the Renaissance