John Elway had his most passing touchdowns in a game against the Vikings on November 18, 1984, with 5 touchdowns.

who is john the most touchdown passes in nfl history
Interpreted as:
Who is john the most touchdown passes in a regular-season game in NFL history?
11/18/1984Elway12/27/1998Elway11/29/1998Elway12/21/1997Elway9/14/1997Elway10/6/1996Elway12/3/1995Elway11/26/1989Elway9/13/1987Elway9/15/1985Elway11/22/1998Elway11/30/1997Elway9/28/1997Elway9/21/1997Elway10/27/1996Elway10/20/1996Elway11/5/1995Elway9/4/1994Elway1/2/1994Elway12/12/1993Elway11/7/1993Elway9/23/1990Elway11/27/1988Elway54444444443333333333333
NAMEDATETMOPPTDCMPATTPCTYDSAVGTD%INTINT%SCKSCKYRATE
John ElwayJohn Elway11/18/1984DENDENvs. MIN
vs.
5161984.221811.526.300.000154.1
John ElwayJohn Elway12/27/1998DENDENvs. SEA
vs.
4263672.23389.411.100.0222138.4
John ElwayJohn Elway11/29/1998DENDEN@ SD
@
4193455.92397.011.838.811380.4
John ElwayJohn Elway12/21/1997DENDENvs. SD
vs.
4172665.427310.515.413.800123.9
John ElwayJohn Elway9/14/1997DENDENvs. STL
vs.
4162857.12478.814.313.6114111.2
John ElwayJohn Elway10/6/1996DENDENvs. SD
vs.
4324178.03237.99.812.4111121.8
John ElwayJohn Elway12/3/1995DENDENvs. JAX
vs.
4223464.72868.411.812.900118.0
John ElwayJohn Elway11/26/1989DENDENvs. SEA
vs.
4101952.621711.421.100.000133.1
John ElwayJohn Elway9/13/1987DENDENvs. SEA
vs.
4223268.833810.612.513.100129.9
John ElwayJohn Elway9/15/1985DENDENvs. NO
vs.
4284365.13538.29.312.3326111.9
John ElwayJohn Elway11/22/1998DENDENvs. OAK
vs.
3172568.01977.912.000.0110131.2
John ElwayJohn Elway11/30/1997DENDEN@ SD
@
3203360.62407.39.100.000113.2
John ElwayJohn Elway9/28/1997DENDEN@ ATL
@
3183354.52437.49.113.031595.9
John ElwayJohn Elway9/21/1997DENDENvs. CIN
vs.
3142653.81626.211.513.821295.4
John ElwayJohn Elway10/27/1996DENDENvs. KC
vs.
3163151.62869.29.713.200102.4
John ElwayJohn Elway10/20/1996DENDENvs. BAL
vs.
3253964.13268.47.712.600105.3
John ElwayJohn Elway11/5/1995DENDENvs. ARI
vs.
3162176.225612.214.300.0110156.0
John ElwayJohn Elway9/4/1994DENDENvs. SD
vs.
3364678.33718.16.524.3430103.9
John ElwayJohn Elway1/2/1994DENDEN@ RAI
@
3253669.436110.08.300.000129.5
John ElwayJohn Elway12/12/1993DENDENvs. KC
vs.
3203066.72217.410.026.721793.9
John ElwayJohn Elway11/7/1993DENDEN@ CLE
@
3172373.924410.613.000.0111147.5
John ElwayJohn Elway9/23/1990DENDENvs. SEA
vs.
3304075.02977.47.500.0216120.5
John ElwayJohn Elway11/27/1988DENDENvs. RAM
vs.
3213658.32727.68.312.81998.4
John ElwayJohn Elway11/29/1987DENDEN@ SD
@
3213265.634710.89.413.100120.2
John ElwayJohn Elway11/16/1987DENDENvs. CHI
vs.
3214052.53418.57.525.00085.5
Results may be incomplete. StatMuse has complete game-level data for passing touchdowns going back to the 1950 season.

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