Question: The 1962 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference during the 1962 college football season, the winning margin was provided by a field goal by Clarkie Mayfield, one of the heroes of the game, who later died at The Beverly Hills Supper Club, fire in Southgate, Kentucky, on which date?

Context paragraphs:
1964 Kentucky Wildcats football team: The 1964 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference during the 1964 college football season.  The Wildcats scored 150 points while allowing 194 points, finishing 5-5 overall, 4-2 in the SEC.

1916 Kentucky Wildcats football team: The 1916 Kentucky Wildcats football team represented the Kentucky Wildcats of the University of Kentucky during the 1916 college football season.  Stoll Field was dedicated for the game with rival Vanderbilt, the season's only loss.  Vanderbilt's quarterback was third-team All-American Irby Curry.  Vanderbilt coach Dan McGugin stated "If you would give me Doc Rodes, I would say he was a greater player than Curry."  The season closed with an upset tie of conference champion and rival Tennessee; an account of which reads "Rodes and McIlvain, Kentucky's quarterback and fullback, played a magnificent game and had they received the proper support from their team, would have piled up a large score against Tennessee."

Beverly Hills Supper Club fire: The Beverly Hills Supper Club fire in Southgate, Kentucky, is the third deadliest nightclub fire in U.S. history.  It occurred on the night of May 28, 1977, during the Memorial Day holiday weekend.  A total of 165 people died and more than 200 were injured as a result of the blaze.  It was the deadliest fire in the United States since 1944, when 168 people were killed in the Hartford circus fire in Hartford, Connecticut.

1980 Kentucky Wildcats football team: The 1980 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference (SEC) during the 1980 NCAA Division I-A football season.  In their eighth season under head coach Fran Curci, the Wildcats compiled a 3–8 record (1–5 against SEC opponents), finished in eighth place in the SEC, and were outscored by their opponents, 280 to 167.  The team played its home games in Commonwealth Stadium in Lexington, Kentucky.

1978 Kentucky Wildcats football team: The 1978 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference (SEC) during the 1978 NCAA Division I-A football season.  In their sixth season under head coach Fran Curci, the Wildcats compiled a 4–6–1 record (2–4 against SEC opponents), finished in a tie for seventh place in the SEC, and outscored their opponents, 193 to 189.  The team played its home games in Commonwealth Stadium in Lexington, Kentucky.

2009 Kentucky Wildcats football team: The 2009 Kentucky Wildcats football team represented the University of Kentucky during the 2009 NCAA Division I FBS football season.  The team was coached by Rich Brooks, in his seventh and ultimately final season at Kentucky, and played its home games at Commonwealth Stadium.  The Wildcats competed in the Southeastern Conference in its eastern division.  They finished the season with a record of 7–6 and 3–5 in conference play, and were defeated by Clemson 21–13 in the Music City Bowl.

1965 Kentucky Wildcats football team: The 1965 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference during the 1965 college football season.  The Wildcats scored 202 points while allowing 160 points, finishing 6-4 overall, 3-3 in the SEC.

2015 Kentucky Wildcats football team: The 2015 Kentucky Wildcats football team (variously "Kentucky", "UK", or "Wildcats") represents the University of Kentucky in the 2015 NCAA Division I FBS football season.  The Wildcats compete in its 122nd season and 82nd as a member of the Southeastern Conference (SEC) as part of its Eastern Division.  The team is led by head coach Mark Stoops, which is his third year coaching the team, and the Wildcats play its home games at Commonwealth Stadium in Lexington, Kentucky.

1994 Kentucky Wildcats football team: The 1994 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference (SEC) during the 1994 NCAA Division I-A football season.  In their fifth season under head coach Bill Curry, the Wildcats compiled a 1–10 record (0–8 against SEC opponents), finished in last place in the Eastern Division of the SEC, and were outscored by their opponents, 405 to 149.  The team won its season opener against Louisville (20–14), but then lost the final ten games of the season, including blowout losses to Florida (7–73), Indiana (29–59), Mississippi State (7–47), and Tennessee (0–52) , following the injury of the Teams Star Running Back transfer from Rutgers U and Kenmore East HS Grad William Bing.  The team played its home games in Commonwealth Stadium in Lexington, Kentucky.

1962 Kentucky Wildcats football team: The 1962 Kentucky Wildcats football team represented the University of Kentucky in the Southeastern Conference during the 1962 college football season.  Coached by Charlie Bradshaw, a Bear Bryant disciple, the team was thinned by his brutal methods from 88 players to just 30.  The team was thus known as the Thin Thirty.  While the team's record was just 3–5–2, it did include a dramatic victory in the season finale against Tennessee in Knoxville, 12–10.  The winning margin was provided by a field goal by Clarkie Mayfield, one of the heroes of the game, who later died in the Beverly Hills Supper Club fire on May 28, 1977.

Supporting paragraphs: 1962 Kentucky Wildcats football team Beverly Hills Supper Club fire
Answer: May 28, 1977