Dennis Rodman had the most games with 36+ minutes played and 5 or fewer points, with 109 games.

most nba games with 36 or more minutes played and 5 or less points by a player
Interpreted as:
most NBA regular-season games with 36 or more minutes played and 5 or less points by a player
RodmanWallaceKiddEatonGrantOakleyBowenDunnBattierBrownTuckerMutomboMasonJacksonSnowCambyMajerleDonaldsonOutlawGreenBoguesDavisJonesGreenBol109806446444340373634323229292727252524242423232222
NAMEGPMINPTSMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%REBASTSTLBLKTOVPF+/-
Dennis RodmanDennis Rodman1094,43033240.63.017.52.60.90.51.81.23.732.80.00.35.60.61.250.81,9052859854194369+206
Ben WallaceBen Wallace803,17825939.73.213.02.11.62.81.21.34.428.20.00.116.70.72.134.11,04316512422798185+358
Jason KiddJason Kidd642,50624539.23.86.99.61.60.33.01.27.815.90.53.513.90.91.370.044461510522189135+17
Mark EatonMark Eaton461,83314939.83.210.31.30.43.81.91.34.130.70.00.00.71.450.0473601917787160
Horace GrantHorace Grant441,73414139.43.28.62.50.91.01.11.35.922.20.00.00.00.61.248.1380108404550124+12
Charles OakleyCharles Oakley431,64415238.23.510.83.51.20.42.41.45.923.10.00.211.10.81.358.94661515218103157+26
Bruce BowenBruce Bowen401,53414538.33.64.01.81.10.61.01.45.424.90.52.421.10.40.763.015971422539107+50
T.R. DunnT.R. Dunn371,43910438.92.87.62.80.81.13.926.90.00.00.00.70.974.328110430104
Shane BattierShane Battier361,40513939.03.95.42.30.91.61.11.45.426.70.42.615.80.60.964.51948433593879+71
P.J. BrownP.J. Brown341,31412638.73.79.82.11.11.21.51.36.520.00.00.00.01.11.573.133371364152105+22
P.J. TuckerP.J. Tucker321,23710138.63.26.91.61.10.61.31.04.821.60.63.217.80.50.868.022152351941106+72
Dikembe MutomboDikembe Mutombo321,24612738.94.012.41.20.53.81.71.45.128.00.00.01.12.348.639737151225494+26
Anthony MasonAnthony Mason291,14510539.53.68.24.30.70.21.71.35.226.00.00.00.91.755.12391242065071-5
Mark JacksonMark Jackson291,11310638.43.74.610.12.00.13.31.26.817.80.22.110.01.01.568.21342925749757+42
Eric SnowEric Snow271,0519238.93.43.96.91.60.21.71.46.123.20.00.40.00.61.151.61061854354685+23
Marcus CambyMarcus Camby271,0388938.53.313.42.41.03.81.21.16.118.90.00.10.01.01.662.836264271023375-10
Dan MajerleDan Majerle2598910639.64.25.34.21.20.31.21.68.219.90.65.111.80.40.752.91321063082947+13
James DonaldsonJames Donaldson259749139.03.611.60.90.51.81.51.44.035.00.00.00.81.272.42892213443761
Bo OutlawBo Outlaw249618540.03.58.53.01.52.52.51.44.432.10.00.00.00.71.839.52057335596078+35
A.C. GreenA.C. Green249429739.34.09.12.01.00.51.51.45.425.60.00.40.01.32.356.42194925123654-42
Muggsy BoguesMuggsy Bogues249348038.93.33.510.92.00.11.91.55.924.60.10.328.60.30.566.7832614834646+10
Dale DavisDale Davis238787538.23.310.41.51.31.51.01.25.621.70.00.00.82.040.42393531352369+30
Charles JonesCharles Jones239104939.62.18.31.81.02.81.00.72.134.70.00.00.71.157.71924124642486
Draymond GreenDraymond Green228288037.63.68.38.42.52.32.71.26.120.10.22.76.81.01.662.918318554506078+100
Manute BolManute Bol228436238.32.88.00.50.36.30.91.24.428.10.00.412.50.30.936.81751271382066
StatMuse has game-level data for minutes played going back to the 1982-83 season.