My mistake, in the last 5 years and 14 Grammys.
2005
Rap Album: “The College Dropout,” Kanye West.
R&B Song: “You Don’t Know My Name,” Alicia Keys, Harold Lilly and Kanye West (Alicia Keys).
Rap Song: “Jesus Walks,” Miri Ben Ari, C. Smith and Kanye West (Kanye West).
2006
Rap Album: “Late Registration,” Kanye West.
Rap Solo Performance: “Gold Digger,” Kanye West.
Rap Song: “Diamonds From Sierra Leone,” D. Harris and Kanye West.
2008:
BEST RAP SOLO PERFORMANCE:
Stronger–Kanye West
BEST RAP PERFORMANCE BY GROUP:
Southside–Common Featuring Kanye West
BEST RAP SONG:
Good Life–Aldrin Davis, Mike Dean, Faheem Najm & Kanye West, songwriters (J. Ingram & Q. Jones, songwriters)(Kanye West Featuring T-Pain)
BEST RAP ALBUM:
Graduation–Kanye West
2009
Rap/Sung Collaboration: Estelle Featuring Kanye West, “American Boy”
Rap Performance by a Duo or Group: Jay-Z and T.I. Featuring Kanye West and Lil Wayne, “Swagga Like Us”
2010
Best Rap/Sung Collaboration: “Run This Town” — Jay-Z, Rihanna & Kanye West
Best Rap Song: “Run This Town” — Jeff Bhasker, Shawn Carter, Robyn Fenty, Kanye West & Ernest Wilson, songwriters (Athanasios Alatas, songwriter) (Jay-Z, Rihanna & Kanye West)
It would seem that the National Academy of Recording Arts and Sciences seems to be comprised of fans, too.
And I believe the “Grammy” year ends in September, so - as was explained- Kanye’s album that came out in November did not qualify for this session.
ETA What my esteemed colleague multimediac17 said 