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was a common year starting on Tuesday of the Gregorian calendar and a common year starting on Sunday of the Julian calendar, the 1805th year of the Common Era (CE) and (AD) designations, the 805th year of the Anno Domini 2nd millennium, the 5th year of the 19th century, and the 6th year of the 1800s decade. As of the start of 1805, the Gregorian calendar was
12 days ahead of the Julian calendar, which remained in localized use until 1923. After thirteen years the First French Empire abolished the French Republican Calendar in favour of the Gregorian calendar.
October 14 – Napoleonic Wars – War of the Third Coalition – Ulm Campaign – Battle of Elchingen: An Austrian corps under Johann von Riesch is defeated by Marshal Ney, near Elchingen, Bavaria.
October 16– 19 – War of the Third Coalition – Ulm Campaign – Battle of Ulm: Austrian General Mack von Leiberich is forced to surrender his entire army to Napoleon, after being surrounded.
October 21 – Napoleonic Wars – War of the Third Coalition – Battle of Trafalgar: The British fleet, led by Admiral Horatio Nelson, defeats a combined French and Spanish fleet off the coast of Spain; however, Admiral Nelson is fatally shot.
October 31 – Sweden, led by King Gustav IV Adolf, declares war on France. 
November 7 – The Lewis and Clark Expedition arrives at the Pacific Ocean.
November 11 – Napoleonic Wars – Battle of Dürenstein: 8,000 French troops attempt to slow the retreat of a vastly superior Russian and Austrian force.
November 16 – Napoleonic Wars – Battle of Schöngrabern: Russian forces, under Pyotr Bagration, delay the pursuit by French troops under Joachim Murat.
November 20 – Beethoven's only opera , in its original form (known retrospectively as Fidelio Leonore), is premiered at the Theater an der Wien in Vienna, which at this time is under French military occupation. November 26 – The Pontcysyllte Aqueduct is opened in Wales; it is 1,007 ft (307 m) long and 126 ft (38 m) tall.
January 8 – Orson Hyde, American religious leader (d. 1878)
January 27 – Samuel Palmer, English artist (d. 1881)
February 13 – Peter Gustav Lejeune Dirichlet, German mathematician (d. 1859)
February 18 – Louis M. Goldsborough, United States Navy admiral (d. 1877)
March 3 – Jonas Furrer, first President of the Swiss Confederation (d. 1861)
March 23 – Sears Cook Walker, American mathematician, astronomer (d. 1853)
March 26 – Shirali Muslimov, World's longest lived person than Jeanne Calment (d. 1973)
April 2 – Hans Christian Andersen, Danish writer (d. 1875)
April 8 – Hugo von Mohl, German botanist (d. 1872)
April 22 – Benito de Soto, Galician pirate (d. 1830)
June 9 – José Trinidad Cabañas, Honduran general, president and national hero (d. 1871) June 22 – Giuseppe Mazzini Italian patriot, statesman, and writer (d. 1872)
July 5 – Robert FitzRoy, English meteorologist, captain and politician (d. 1865)
July 29 – Alexis de Tocqueville, French historian (d. 1859)
July 30 – Rudolf Wagner, German anatomist, pathologist (d. 1864)
August 4 – William Rowan Hamilton, Irish physicist (d. 1865)
September 19 – John Stevens Cabot Abbott, American historian, pastor, and pedagogical writer (d. 1877)
September 27 – George Müller, Prussian evangelist, founder of the Ashley Down orphanage in England (d. 1898)
November 14 – Fanny Mendelssohn, German composer, pianist (d. 1847)
November 28 – John Lloyd Stephens, American traveler, diplomat and Mayanist archaeologist (d. 1852)
December 2 – Cicero Price, American commodore (d. 1888)
December 10 – William Lloyd Garrison, American abolitionist (d. 1879)
December 12 – Henry Wells, founder of Wells Fargo (d. 1878)
December 22 – John Obadiah Westwood, English entomologist (d. 1893)
December 23 – Joseph Smith, founder of The Church of Jesus Christ of Latter Day Saints Church and Latter Day Saint movement (d. 1844)
December 31 – Jeanne Deroin, French socialist, feminist (d. 1894) date unknown
January 9 – Noble Wimberly Jones, American Continental Congressman (b. 1723)
January 17 – Paschen von Cossel, German lawyer (b. 1714)
January 18 – John Moore (archbishop of Canterbury) (b. 1730)
January 23 – Claude Chappe, French telecommunication pioneer (b. 1763)
February 20 – Justus Claproth, German jurist, inventor of the de-inking process of recycled paper (b. 1728)
February 25 – Thomas Pownall, English colonial statesman (b. 1722)
March 4 – Jean-Baptiste Greuze, French painter (b. 1725)
May 7 – William Petty, 2nd Earl of Shelburne, Prime Minister of the United Kingdom (b. 1737)
May 9 – Friedrich Schiller, German playwright (b. 1759)
May 12 – Ferdinand von Hompesch zu Bolheim, 71st Grandmaster of the Order of Malta (b. 1744)
May 25 – William Paley, English philosopher (b. 1743)
May 25 – Anna Maria Rückerschöld, Swedish author (d. 1725)
May 28 – Luigi Boccherini, Tuscan-born composer (b. 1743) June 19 – Louis-Jean-François Lagrenée, French painter (b. 1724)
August 3 – Christopher Anstey, English writer (b. 1724)
August 28 – Alexander Carlyle, Scottish church leader (b. 1722)
October 5 – Charles Cornwallis, 1st Marquess Cornwallis, British general (b. 1738)
October 5 – Eleonore Prochaska, German heroine soldier (b. 1785)
October 21 – Horatio Nelson, British admiral (mortally wounded in battle) (b. 1758)
December 16 – Saverio Cassar, Gozitan priest, rebel leader (b. 1746)
December 23 – Pehr Osbeck, Swedish explorer, naturalist (b. 1723)
December 23 – Geneviève Thiroux d'Arconville, French novelist, translator and chemist (b. 1720) date unknown
^ Karen Jones and John Wills,
The American West: Competing Visions (Edinburgh University Press, 2009) p17
^ Kinley Brauer and William E. Wright,
Austria in the Age of the French Revolution, 1789-1815 (Berghahn Books, 1990) p11
^ "Baird, David", in
A New General Biographical Dictionary, Volume 3, ed. by Hugh James Rose (T. Fellowes, 1857) p20
Tales of the Wars; Or, Naval and Military Chronicle (William Mark Clark, 1836) p329
The Englishman's library: comprising a series of historical, biographical, and national information (Charles Knight, 1824) p165
^ H. Arnold Barton,
Scandinavia in the Revolutionary Era: 1760–1815 (University of Minnesota Press, 1986) p267
^ Thomas Carlyle,
The French Revolution (Courier Corporation, 2012) p210