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, a Federalist, 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.
1805 Delaware's at-large congressional district special election|
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Broom took his seat with the rest of the 9th Congress on December 2, 1805.
| County | Broom# | Broom% | Hall# | Hall% | Starr# | Starr% | Richie# | Richie% | Total |
| Kent | 966 | 61.06% | 593 | 37.48% | 23 | 1.45% | | | 1,582 |
| New Castle | 683 | 32.63% | 1,407 | 67.22% | 1 | 0.05% | 2 | 0.10% | 2,093 |
| Sussex | 1,362 | 66.63% | 682 | 33.37% | | | | | 2,044 |