Drew Brees had the most games with 5+ passing touchdowns, with 11 games.

who has the most career 5+ passing td games
Interpreted as:
Who has the most career 5+ passing td regular-season games?
Brees Brady Manning Mahomes Roethlisberger Marino Wilson Rodgers Blanda Jackson Stafford Favre Moon Watson Newton Culpepper Kelly Montana Krieg Fouts Meredith Dawson Johnson Jurgensen Goff Winston Manning 0 1 2 3 4 5 6 7 8 9 10 11 11 9 9 6 6 6 5 5 5 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 2 2 2
NAME GP TD CMP ATT PCT YDS AVG YDS/G TD% INT INT% SCK SCKY RATE
Drew Brees Drew Brees 11 58 296 381 77.7 3,963 10.4 360.3 15.2 4 1.0 10 53 145.2
Tom Brady Tom Brady 9 47 251 337 74.5 3,283 9.7 364.8 13.9 1 0.3 16 104 143.1
Peyton Manning Peyton Manning 9 49 219 315 69.5 3,230 10.3 358.9 15.6 7 2.2 6 43 133.1
Patrick Mahomes Patrick Mahomes 6 32 176 235 74.9 2,264 9.6 377.3 13.6 4 1.7 5 41 137.1
Ben Roethlisberger Ben Roethlisberger 6 32 146 188 77.7 1,927 10.3 321.2 17.0 1 0.5 10 64 146.7
Dan Marino Dan Marino 6 31 150 245 61.2 2,333 9.5 388.8 12.7 5 2.0 5 34 123.9
Russell Wilson Russell Wilson 5 25 121 173 69.9 1,618 9.4 323.6 14.5 1 0.6 11 73 136.5
Aaron Rodgers Aaron Rodgers 5 27 112 159 70.4 1,698 10.7 339.6 17.0 0 0.0 4 26 144.9
George Blanda George Blanda 5 28 87 158 55.1 1,554 9.8 310.8 17.7 6 3.8 112.7
Lamar Jackson Lamar Jackson 4 20 65 84 77.4 1,026 12.2 256.5 23.8 0 0.0 5 19 157.0
Matthew Stafford Matthew Stafford 4 20 117 176 66.5 1,614 9.2 403.5 11.4 6 3.4 8 48 119.4
Brett Favre Brett Favre 4 21 94 143 65.7 1,279 8.9 319.8 14.7 6 4.2 9 47 116.2
Warren Moon Warren Moon 4 20 94 141 66.7 1,316 9.3 329.0 14.2 5 3.5 5 38 121.3
Deshaun Watson Deshaun Watson 3 15 60 84 71.4 926 11.0 308.7 17.9 0 0.0 3 13 147.1
Cam Newton Cam Newton 3 15 74 120 61.7 917 7.6 305.7 12.5 1 0.8 6 60 121.4
Daunte Culpepper Daunte Culpepper 3 15 79 110 71.8 1,063 9.7 354.3 13.6 2 1.8 7 16 134.2
Jim Kelly Jim Kelly 3 16 66 99 66.7 1,118 11.3 372.7 16.2 6 6.1 5 46 119.0
Joe Montana Joe Montana 3 16 94 140 67.1 1,333 9.5 444.3 11.4 3 2.1 13 86 126.9
Dave Krieg Dave Krieg 3 15 65 98 66.3 821 8.4 273.7 15.3 3 3.1 4 35 119.1
Dan Fouts Dan Fouts 3 16 79 122 64.8 1,038 8.5 346.0 13.1 2 1.6 3 22 124.2
Don Meredith Don Meredith 3 15 48 72 66.7 983 13.7 327.7 20.8 1 1.4 143.5
Len Dawson Len Dawson 3 16 56 93 60.2 976 10.5 325.3 17.2 4 4.3 117.7
Charley Johnson Charley Johnson 3 17 44 83 53.0 986 11.9 328.7 20.5 5 6.0 110.2
Sonny Jurgensen Sonny Jurgensen 3 15 53 90 58.9 1,155 12.8 385.0 16.7 7 7.8 110.4
Jared Goff Jared Goff 2 10 50 67 74.6 743 11.1 371.5 14.9 0 0.0 3 24 150.1
StatMuse has game-level data for passing touchdowns going back to the 1950 season.

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AFC North W L T PCT
1
Ravens Ravens
13 4 0 .765
2
Browns Browns
11 6 0 .647
AFC East W L T PCT
1
Bills Bills
11 6 0 .647
2
Dolphins Dolphins
11 6 0 .647
AFC West W L T PCT
1
Chiefs Chiefs
11 6 0 .647
2
Raiders Raiders
8 9 0 .471
AFC South W L T PCT
1
Texans Texans
10 7 0 .588
2
Jaguars Jaguars
9 8 0 .529
NFC North W L T PCT
1
Lions Lions
12 5 0 .706
2
Packers Packers
9 8 0 .529
NFC West W L T PCT
1
49ers 49ers
12 5 0 .706
2
Rams Rams
10 7 0 .588
NFC East W L T PCT
1
Cowboys Cowboys
12 5 0 .706
2
Eagles Eagles
11 6 0 .647
NFC South W L T PCT
1
Buccaneers Buccaneers
9 8 0 .529
2
Saints Saints
9 8 0 .529