However, this is a bit of a controversial statement. Brando did not accept the award himself, instead sending Sacheen Littlefeather, a Native American activist, to decline the award on his behalf, in protest of the film industry's portrayal of Native Americans. This speech was much shorter than 5 minutes and 21 seconds, but the time allotted to the ceremony for Brando's absence and Littlefeather's speech, and the subsequent commotion that followed, added up to that total.
Therefore, whether it's technically considered a "speech" is debatable.
If you're looking for the longest speech by someone actually accepting the award, that would be 5 minutes and 13 seconds, delivered by Roberto Benigni for his Best Director win in 1999 for his film "Life Is Beautiful".