They won a [token] Grammy in 1999 when “I Want You Back” was entered into the Hall of Fame for its lyrics, written by Freddie Perren, Deke Richards, Alphonzo Mizell and Berry Gordy. “I Want You Back” reached #1 in 1970 but was not honored until almost 30 years later. However, none of The Jacksons other songs or recordings ever won a Grammy.
From Wikipedia:
The Jackson 5 or Jackson Five (later known as The Jacksons) was an American popular music family group from Gary, Indiana. Formed in 1964 under the name the Jackson Brothers, the founding members were Jackie, Tito and Jermaine. Marlon and Michael would later join, and the band’s name would be changed to The Jackson 5. After participating in talent shows and the chitlin’ circuit, they entered the professional music scene in 1967 signing with Steeltown Records and releasing two singles. In 1969 they left Steeltown Records in order to sign with Motown.
Among the first groups of black American performers to attain a crossover following, preceded by the Supremes, the Four Tops and the Temptations, the group made history in 1970 as the first recording act whose first four singles reached No. 1 on the Billboard Hot 100, with the songs: “I Want You Back”, “ABC”, “The Love You Save” and “I’ll Be There”. Scoring 17 top forty singles on the Hot 100, after continuing with further hits such as “Never Can Say Goodbye” and “Dancing Machine”, most of the group with the exception of Jermaine, left Motown for Epic Records in 1975, where, with brother Randy taking Jermaine’s place, they released five albums between 1976 and 1981, including the hit albums, Destiny (1978) and Triumph (1980) and the hit singles, “Enjoy Yourself”, “Shake Your Body (Down to the Ground)” and “Can You Feel It.” In 1983, Jermaine reunited with the band to perform on Motown 25: Yesterday, Today, Forever and subsequently released the Victory album the following year. After the end of their tour to promote the album, Michael Jackson and Marlon Jackson promptly left the group. The remaining four released the poorly received 2300 Jackson Street album in 1989 before being dropped from their label.
Inducted to the Rock and Roll Hall of Fame in 1997 and the Vocal Group Hall of Fame in 1999, the Jacksons reunited in 2001 on Michael’s 30th anniversary television special. Following the death of Michael Jackson in 2009, the four eldest of the brothers embarked on their Unity Tour in 2012.
Influenced by The Temptations, The Supremes, James Brown, Frankie Lymon & The Teenagers and Sly & The Family Stone, the group eventually served as the inspiration for several generations of boy bands, including New Edition, Menudo, New Kids on the Block, N*SYNC, the Jonas Brothers, Backstreet Boys, One Direction, and many more.
https://en.wikipedia.org/wiki/The_Jackson_5