Karl Malone had the most games with 20+ points and 5+ rebounds, with 1,116 games.

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most games with 20 points 5 reb 5 asst
Interpreted as:
most regular-season games by a player with 20 or more points 5 or more reb 5 asst
MaloneJamesO'NealNowitzkiOlajuwonEwingBarkleyJordanDuncanDurantGarnettBryantWilkinsAnthonyRobinsonPierceWestbrookWebberJamisonDrexlerBirdAldridgeGasolCummingsMalone1.1k939811777739661652645634617614612607599544505483477468467467466440433432
NAMEGPPTSREBMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINASTSTLBLKTOVPF+/-
Karl MaloneKarl Malone111631,56412,11538.728.310.93.61.50.83.110.419.453.50.10.229.77.510.075.343,1884,0471,6319333,4613,524+2737
LeBron JamesLeBron James93927,6427,81539.129.48.37.51.70.83.610.720.651.91.74.735.76.38.673.836,7427,0531,5657323,3441,772+6006
Shaquille O'NealShaquille O'Neal81123,0929,88937.928.512.22.80.72.52.911.319.059.50.00.05.05.910.953.830,7302,2785372,0552,3202,765+3915
Dirk NowitzkiDirk Nowitzki77720,8777,16438.226.99.22.80.91.02.09.418.850.31.63.742.26.47.288.729,6542,1837167611,5181,969+5209
Hakeem OlajuwonHakeem Olajuwon73920,2989,20739.027.512.52.81.93.53.310.920.254.10.00.120.55.67.673.428,8362,0961,4392,5632,4112,758+372
Patrick EwingPatrick Ewing66118,0917,48138.527.411.32.21.12.93.310.720.053.60.00.119.05.97.875.825,4291,4447281,9192,1882,370+486
Charles BarkleyCharles Barkley65217,9718,29639.627.612.74.21.80.93.49.716.957.40.72.329.67.49.974.825,7932,7441,1536132,1972,045+444
Michael JordanMichael Jordan64521,1515,00939.832.87.85.62.50.92.812.324.450.40.61.833.37.69.183.525,6743,5971,6145731,8301,716+984
Tim DuncanTim Duncan63416,2217,88038.425.612.43.20.82.52.89.918.154.40.00.217.65.88.172.024,3202,0055181,5571,7701,698+4321
Kevin DurantKevin Durant61718,2515,18238.229.68.44.41.21.23.310.019.850.62.15.339.47.58.488.623,5462,7017157192,0231,256+3552
Kevin GarnettKevin Garnett61415,1977,47839.124.812.24.61.41.62.69.818.253.80.20.633.05.06.280.624,0292,8538639881,5721,563+3316
Kobe BryantKobe Bryant61218,8704,40240.130.87.25.21.60.63.310.723.146.51.64.534.97.89.383.824,5483,1689913472,0211,617+2818
Dominique WilkinsDominique Wilkins60718,3385,08738.630.28.42.80.711.223.148.50.82.335.47.08.582.423,4471,7014231,218-28
Carmelo AnthonyCarmelo Anthony59916,8774,70137.928.27.83.11.10.52.810.021.147.51.53.937.76.68.082.622,6981,8546663251,6551,800+2001
David RobinsonDavid Robinson54415,0536,45338.527.711.93.01.53.42.99.818.054.60.00.227.18.010.675.620,9441,6158391,8721,5671,631+595
Paul PiercePaul Pierce50513,7283,88539.227.27.74.11.60.63.08.818.547.72.15.141.87.49.181.319,7772,0668033241,5361,477+2046
Russell WestbrookRussell Westbrook48313,8264,46036.728.69.29.31.80.34.510.121.946.21.54.733.26.88.579.917,7224,4818481542,1941,291+1882
Chris WebberChris Webber47712,1985,16940.325.610.84.71.61.63.010.720.951.00.41.231.03.95.768.119,2272,2367767781,4091,604+1638
Antawn JamisonAntawn Jamison46812,1594,50840.026.09.61.91.10.41.89.919.949.51.53.740.44.76.375.218,7338795102028591,226+185
Clyde DrexlerClyde Drexler46712,4373,74538.526.68.06.22.30.73.010.119.751.11.02.735.95.67.079.417,9722,9071,0723451,3811,475+258
Larry BirdLarry Bird46713,6024,79240.029.110.36.711.321.652.31.02.541.75.56.189.718,6703,1451,108
LaMarcus AldridgeLaMarcus Aldridge46611,9904,61436.925.79.92.20.81.21.710.419.353.90.30.735.04.75.782.917,2151,0413835427741,110+2849
Pau GasolPau Gasol44010,6694,60537.624.210.53.40.62.02.59.316.257.40.10.340.25.67.277.816,5561,5082628651,0781,018+1733
Terry CummingsTerry Cummings43311,1424,20536.225.79.72.510.520.152.50.14.66.274.615,6551,0731,548+24
Moses MaloneMoses Malone43211,2925,61737.026.113.01.51.48.716.951.20.00.110.78.810.980.515,9946685921,030
StatMuse has game-level data for rebounds going back to the 1982-83 season.