1755 in Denmark

• Monarch – Frederick V{{cite web |title=Frederick V {{!}} king of Denmark and Norway |url=https://www.britannica.com/biography/Frederick-V-king-of-Denmark-and-Norway |website=Encyclopedia Britannica |access-date=18 November 2019 |language=en}}
• Prime minister – Johan Ludvig Holstein-Ledreborg

• 24 November – The company now known as Iver C. Weilbach & Co. A/S is founded when flag, sail and compass maker Iver Jensen Borger sets up his own maritime supplier business in Copenhagen

• 5 February – Caroline Müller, operatic mezzo-soprano, actress and dancer (died 1826)
• 3 March {{ndash}} Cathrine Marie Gielstrup, stage actress (died 1792)
• 19 September {{ndash}} David Amsel Meyer, businessman and financial advisor (died 1813)
• 17 October - Envold de Falsen, lawyer, poet, actor and statesman (died 1808).{{cite encyclopedia|title=Envold De Falsen |encyclopedia=Norsk biografisk leksikon|first=Paul |last=Thyness |editor=Helle, Knut|publisher=Kunnskapsforlaget |location=Oslo |url=http://www.snl.no/.nbl_biografi/Envold_De_Falsen/utdypning |language=no |access-date=30 October 2012}}
• 16 November {{ndash}} Joachim-Daniel Preisler, actor (died 1809)

• 5 February {{ndash}} Gideon von der Lühe, county governor (born 1704)
• 12 February {{ndash}} Frederik Fabritius, goldsmith (born 1683)
• 28 February – Johannes Erasmus Iversen, composer (born 1713)

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