Question: Princess Christina Margarethe of Hesse was the eldest daughter of what fifth son of Prince Frederick Charles of Hesse and Princess Margaret of Prussia?

Context paragraphs:
Alexander Frederick, Landgrave of Hesse: Alexander Frederick, Landgrave of Hesse (German: "Alexander Friedrich Wilhelm Albrecht Georg Landgraf von Hessen" 25 January 1863, Copenhagen – 26 March 1945) was a Hesse-Kassel and Prussian Prince.  He was the son of Prince Frederick William of Hesse-Kassel and Princess Anna of Prussia.  From 1888–1925 he was Head of the House of Hesse, but abdicated his position to his brother Prince Frederick Charles of Hesse.  He was visually handicapped from birth, and this, in addition to his morganatic marriage, played a part in his decision to abdicate.

Frederick Augustus II, Grand Duke of Oldenburg: Frederick Augustus II (16 November 1852 in Oldenburg – 24 February 1931 in Rastede) was the last ruling Grand Duke of Oldenburg.  He married Princess Elisabeth Anna of Prussia, daughter of Princess Maria Anna of Anhalt-Dessau and Prince Frederick Charles of Prussia.  After her death, he married Elisabeth Alexandrine of Mecklenburg-Schwerin.

Princess Charlotte of Prussia: Princess Charlotte of Prussia (Viktoria Elisabeth Auguste Charlotte; 24 July 1860 – 1 October 1919) was Duchess Consort of Saxe-Meiningen as the wife of Bernhard III, the duchy's last ruler.  Born at the "Neues Palais" in Potsdam, she was the second child and eldest daughter of Prince Frederick of Prussia, a member of the House of Hohenzollern who became Crown Prince of Prussia in 1861 and German Emperor in 1888.  Through her mother Victoria, Princess Royal, Charlotte was the eldest granddaughter of the British monarch Queen Victoria and her consort Prince Albert of Saxe-Coburg and Gotha.

Princess Christina Margarethe of Hesse: Princess Christina Margarethe of Hesse (German: "Prinzessin Christina Margarethe von Hessen" ; 10 January 1933 – 22 November 2011) was the eldest daughter of Prince Christoph of Hesse and Princess Sophie of Greece and Denmark.  From 1956 to 1962, she was married to Prince Andrew of Yugoslavia, with whom she had two children.  Her second marriage to Robert Floris van Eyck, a Dutch artist based in London, lasted from 1962 to 1986.

Prince Christoph of Hesse: Christoph Ernst August of Hesse (Frankfurt, 14 May 1901 – Apennine Mountains near Forlì, 7 October 1943) was the fifth son of Prince Frederick Charles of Hesse and Princess Margaret of Prussia.  He was a German SS officer killed accidentally during World War II.

Princess Marie of Prussia (1855–1888): Princess Marie of Prussia ("Marie Elisabeth Louise Frederika of Prussia"; 14 September 1855, Marmorpalais, Potsdam – 20 June 1888, Dresden), was a princess of the House of Hohenzollern.  She was the daughter of Prince Frederick Charles of Prussia and later became second wife of Prince Henry of the Netherlands then the first wife of Prince Albert of Saxe-Altenburg.  She was also the great-niece of Wilhelm I, German Emperor.

Prince Friedrich Karl of Prussia (1828–85): Prince Friedrich Carl Nicolaus of Prussia (20 March 1828 – 15 June 1885) was the son of Prince Charles of Prussia (1801–1883) and his wife, Princess Marie of Saxe-Weimar-Eisenach (1808–1877).  Prince Frederick Charles was a grandson of King Frederick William III of Prussia and a nephew of Frederick William IV and William I.  He was born at Schloss Klein in Berlin.

Prince Sigismund of Prussia (1864–1866): Prince Sigismund of Prussia (Franz Friedrich Sigismund; 15 September 1864 – 18 June 1866) was the fourth child and third son of Crown Prince Frederick William of Prussia (later King of Prussia and German Emperor as Frederick III), and Victoria, Princess Royal, eldest daughter of the British Queen Victoria.

Princess Irene of Hesse and by Rhine: Princess Irene of Hesse and by Rhine ("Irene Luise Marie Anne, Princess of Hesse and by Rhine", 11 July 1866 – 11 November 1953) was the third child and third daughter of Princess Alice of the United Kingdom and Louis IV, Grand Duke of Hesse and by Rhine.  Her maternal grandparents were Queen Victoria and Prince Albert of Saxe-Coburg and Gotha.  Her paternal grandparents were Prince Charles of Hesse and by Rhine and Princess Elizabeth of Prussia.  She was the wife of Prince Henry of Prussia, a younger brother of Wilhelm II, German Emperor and her first cousin.  The SS "Prinzessin Irene", a liner of the North German Lloyd was named after her.

Princess Margaret of Prussia: Princess Margaret of Prussia (Margarete Beatrice Feodora; 22 April 1872 – 22 January 1954) was a daughter of Frederick III, German Emperor and Victoria, Princess Royal, and the younger sister of Emperor Wilhelm II and a granddaughter of Queen Victoria.  She married Prince Frederick Charles of Hesse, the elected King of Finland, making her the would-be Queen of Finland had he not decided to reject the throne.  In 1926 they became Landgrave and Landgravine of Hesse.  She lost three sons in both World Wars I and II.

Supporting paragraphs: Princess Christina Margarethe of Hesse Prince Christoph of Hesse
Answer: Prince Christoph of Hesse