Dennis Rodman had the most games with 45+ minutes played and 5 or fewer points, with 17 games.

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most nba games with 45 or more minutes played and 5 or less points by a player
Interpreted as:
most NBA regular-season games with 45 or more minutes played and 5 or less points by a player
RodmanWallaceGrantOutlawWilliamsWalkerAlstonBrownBowenDavisMasonFisherKiddHorryJonesMillsMajerleCageKiteJonesEatonDunnBullockRivers1784333222222222222222211
NAMEGPMINPTSMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%REBASTSTLBLKTOVPF+/-
Dennis RodmanDennis Rodman177884646.42.720.12.80.70.91.81.14.425.70.10.512.50.40.943.83414712153070+40
Ben WallaceBen Wallace83772647.13.314.31.61.52.41.01.45.525.00.00.10.00.52.025.0114131219819+9
Horace GrantHorace Grant4186946.52.312.02.81.01.31.80.83.521.40.00.30.00.81.075.0481145716+8
Bo OutlawBo Outlaw31411247.04.08.35.70.73.02.31.34.728.60.00.01.32.066.7251729712-12
Lorenzo WilliamsLorenzo Williams31481249.34.015.01.31.73.72.01.74.041.70.00.00.72.328.6454511610
Darrell WalkerDarrell Walker3139646.32.09.79.33.00.73.00.74.714.30.00.30.00.71.350.0292892910
Rafer AlstonRafer Alston299749.63.55.08.52.00.52.01.58.517.60.53.016.70.00.010174144-10
P.J. BrownP.J. Brown293746.53.512.54.51.50.51.51.06.016.70.00.01.52.075.02593138+4
Bruce BowenBruce Bowen291945.54.54.51.51.00.50.51.56.523.11.05.020.00.52.025.0932115+15
Antonio DavisAntonio Davis290645.03.014.51.51.50.50.50.58.06.30.00.02.03.066.72933117+8
Anthony MasonAnthony Mason291745.53.58.54.02.50.50.51.07.014.30.00.01.52.075.01785114+13
Derek FisherDerek Fisher291745.53.53.06.02.50.52.00.57.56.70.02.00.02.53.083.36125145+34
Jason KiddJason Kidd2921046.05.07.513.02.00.06.02.013.514.80.57.07.10.51.050.0152640126+2
Robert HorryRobert Horry292946.04.511.03.03.01.03.52.010.519.00.53.514.30.00.02266279+22
Popeye JonesPopeye Jones291445.52.011.50.52.01.02.01.05.020.00.01.00.00.00.023142410-3
Chris MillsChris Mills291745.53.52.04.01.00.02.51.59.515.80.02.00.00.51.050.0482053-11
Dan MajerleDan Majerle294847.04.06.07.53.51.02.51.012.08.30.55.59.11.53.542.912157253+4
Michael CageMichael Cage291745.53.513.02.01.50.52.51.02.540.00.00.01.54.037.52643157
Greg KiteGreg Kite293946.54.510.01.00.00.51.02.06.530.80.00.00.51.050.02020128
Charles JonesCharles Jones294247.01.013.01.51.07.02.50.02.00.00.00.01.01.0100.026321458
Mark EatonMark Eaton292646.03.012.00.01.01.00.51.53.050.00.00.00.00.02402218
T.R. DunnT.R. Dunn291445.52.010.52.52.50.50.00.53.514.30.00.01.01.0100.02155108
Reggie BullockReggie Bullock146545.75.05.01.00.00.01.02.09.022.21.05.020.00.00.05100140
Austin RiversAustin Rivers146546.35.05.05.00.01.00.02.08.025.01.06.016.70.00.0550104+10
Wilson ChandlerWilson Chandler148048.20.09.02.01.00.03.00.03.00.00.02.00.00.00.0921035+1
StatMuse has game-level data for minutes played going back to the 1982-83 season.