A special election was held in Delaware's at-large congressional district on October 1, 1805 to fill a vacancy resulting from the resignation of James A. Bayard (F) upon election to the Senate. Bayard had earlier served in the House in the 5th, 6th, and 7th Congresses before being narrowly defeated for re-election in 1802 by Caesar A. Rodney, whom he, in turn, defeated in 1804.
Election returns
Broom took his seat with the rest of the 9th Congress on December 2, 1805
References
Delaware's at-large congressional district special election, 1805 Wikipedia(Text) CC BY-SA