Question: The 1996 Air Force Falcons finished the season with a 5–3 record in in an American collegiate athletic conference formed on what date?

Context paragraphs:
1994 Air Force Falcons football team: The 1994 Air Force Falcons football team represented the United States Air Force Academy in the 1994 NCAA Division I-A football season.  The team was led by 11th-year head coach Fisher DeBerry and played its home games at Falcon Stadium.  It finished the season with an 8–4 record overall and a 5–3 record in Western Athletic Conference games.

1955 Air Force Falcons football team: The 1955 Air Force Falcons football team represented the United States Air Force Academy in the 1955 college football season.  The Falcons did not have an official stadium during the season, and remained without one until the 1962 season when Falcon Stadium opened.  They were led by first year head coach Robert V. Whitlow and played the first season for the Air Force falcons football program.  The Falcons were independent, and played only freshmen teams of other schools.  Air Force finished with a record of 4–4.

1982 Air Force Falcons football team: The 1982 Air Force Falcons football team represented the United States Air Force Academy in the 1982 NCAA Division I-A football season.  The team was led by fourth-year head coach Ken Hatfield and played its home games at Falcon Stadium.  It finished the regular season with a 7–5 overall record and a 4–3 record in Western Athletic Conference games.  The team was selected to play in the Hall of Fame Classic, in which it defeated Vanderbilt 36–28.

1956 Air Force Falcons football team: The 1956 Air Force Falcons football team represented the United States Air Force Academy in the 1956 college football season.  The Falcons did not have an official stadium during the season, and remained without one until the 1962 season when Falcon Stadium opened.  They were led by first year head coach Buck Shaw and played the second season for the Air Force falcons football program.  The Falcons were independent, and finished with a record of 6–2–1.

1980 Air Force Falcons football team: The 1980 Air Force Falcons football team represented the United States Air Force Academy in the 1981 NCAA Division I-A football season.  The team was led by second-year head coach Ken Hatfield and played its home games at Falcon Stadium.  It finished the regular season with a 2–9–1 overall record and a 1–3 record in Western Athletic Conference games.

2008 Air Force Falcons football team: The 2008 Air Force Falcons football team represented the United States Air Force Academy during the 2008 NCAA Division I FBS football season.  Air Force competed as a member of the Mountain West Conference (MWC).  The team was led by second-year head coach Troy Calhoun.  The Falcons finished the regular season with an 8–4 record to attain bowl eligibility.  Air Force secured a berth in the Armed Forces Bowl for the second consecutive season, and played a re-match of an earlier regular season game against Houston.  Air Force lost the re-match, 34–28, which achieved their first bowl win since 1980.

1981 Air Force Falcons football team: The 1981 Air Force Falcons football team represented the United States Air Force Academy in the 1981 NCAA Division I-A football season.  The team was led by third-year head coach Ken Hatfield and played its home games at Falcon Stadium.  It finished the regular season with a 4–7 overall record and a 2–3 record in Western Athletic Conference games.

1984 Air Force Falcons football team: The 1984 Air Force Falcons football team represented the United States Air Force Academy in the 1984 NCAA Division I-A football season.  The team was led by first-year head coach Fisher DeBerry and played its home games at Falcon Stadium.  It finished the regular season with a 7–4 record overall and a 4–3 record in Western Athletic Conference games.  The team was selected to play in the Independence Bowl, in which it defeated Virginia Tech.

Western Athletic Conference: The Western Athletic Conference (WAC) is an American collegiate athletic conference formed on July 27, 1962 and affiliated with the National Collegiate Athletic Association (NCAA) Division I.  The WAC covers a broad expanse of the western United States, with member institutions located in Arizona, California, New Mexico, Utah, and Washington, along with the "non-western" states of Missouri and Illinois (traditionally associated with the Midwest), as well as Texas (traditionally associated with the Southwest).

1996 Air Force Falcons football team: The 1996 Air Force Falcons football team competed for the United States Air Force Academy in the 1996 NCAA Division I-A football season.  The team was led by 13th-year head coach Fisher DeBerry and played its home games at Falcon Stadium.  It finished the season with a 6–5 record overall and a 5–3 record in Western Athletic Conference games.

Supporting paragraphs: 1996 Air Force Falcons football team Western Athletic Conference
Answer: July 27, 1962