Representatives had been elected in December 1796 to a term in the 5th United States Congress beginning on March 4, 1795.

Of the incumbents, Havens, Livingston, Van Cortlandt, Elmendorf and Glen were re-elected; Brooks and Williams were defeated; and Hezekiah L. Hosmer, John E. Van Alen and James Cochran did not run for re-election.

After some time both terms got more and more confused, and sometimes used together as "Democratic Republicans" which later historians have adopted (with a hyphen) to describe the party from the beginning, to avoid confusion with both the later established and still existing Democratic and Republican parties.

[3] Jonathan N. Havens, who had been re-elected to a third term, died on October 25, 1799, shortly before Congress met.

A special election to fill the vacancy was held in the 1st District in December 1799, and was won by John Smith, of the same party as Havens.