Aaron Rodgers has the most games with 10+ rushing yards and 400+ passing yards, with 8 games.

most career games with 10 rush yards 400 pass yards and 5 pass tds (including postseason)
Interpreted as:
most career games with 10 or more rush yards 400 or more pass yards and 5 pass tds by a player (including postseason)
RodgersPrescottBradyFitzpatrickRoethlisbergerLuckFolesStaffordRiversMontanaJurgensenMurrayAllenMahomesWilsonWatsonCarrRyanVickNewtonOrtonCasselBrees87544333333222222222222
NAMEGPRUSH YDSPASS YDSTDCMPATTPCTAVGYDS/GTD%INTINT%SCKSCKYRATE
Aaron RodgersAaron Rodgers82183,3842223836265.79.3423.06.151.424134110.3
Dak PrescottDak Prescott71263,1392023534268.79.2448.45.872.01181108.6
Tom BradyTom Brady5672,1581217826367.78.2431.64.631.11481103.1
Ryan FitzpatrickRyan Fitzpatrick41201,6361111617765.59.2409.06.274.083599.4
Ben RoethlisbergerBen Roethlisberger4631,804913720467.28.8451.04.462.994397.3
Andrew LuckAndrew Luck3821,307119515262.58.6435.77.253.3749100.4
Nick FolesNick Foles3651,245128813863.89.0415.08.732.2533112.7
Matthew StaffordMatthew Stafford3601,31658713564.49.7438.73.732.253499.5
Philip RiversPhilip Rivers3351,28678813465.79.6428.75.221.5637108.0
Joe MontanaJoe Montana3391,297118011669.011.2432.39.532.61062127.0
Sonny JurgensenSonny Jurgensen3461,248117312757.59.8416.08.764.7100.1
Kyler MurrayKyler Murray2608066567277.811.2403.08.334.2438123.7
Josh AllenJosh Allen2338307557375.311.4415.09.600.0833144.2
Patrick MahomesPatrick Mahomes2569409709573.79.9470.09.533.2536123.1
Russell WilsonRussell Wilson2818586589163.79.4429.06.611.126111.9
Deshaun WatsonDeshaun Watson21148289476374.613.1414.014.334.8535136.1
Derek CarrDerek Carr22893076911162.28.4465.06.300.0215109.8
Matt RyanMatt Ryan2299517598073.811.9475.58.811.3425137.0
Michael VickMichael Vick21098444538264.610.3422.04.911.2428110.0
Cam NewtonCam Newton2718543528362.710.3427.03.644.884789.1
Kyle OrtonKyle Orton22790726911361.18.0453.51.843.53777.6
Matt CasselMatt Cassel2768156609463.88.7407.56.411.1521108.2
Drew BreesDrew Brees22584256610364.18.2421.04.943.952789.5
Daunte CulpepperDaunte Culpepper2358298517270.811.5414.511.134.2742128.8
Matt HasselbeckMatt Hasselbeck2588635649368.89.3431.55.422.2537107.1
StatMuse has game-level data for rushing yards going back to the 1960 season.

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