Question: Frederick V, Count of Zollern died at which ancestral seat atop Mount Hohenzollern?

Context articles: Burkhard I, Count of Zollern
Northern Ice Field (Mount Kilimanjaro)
Frederick VII, Count of Zollern
Hohenzollern Castle
Conrad I, Burgrave of Nuremberg
Frederick IV, Count of Zollern
Frederick II of Zollern
Frederick VI, Count of Zollern
Frederick V, Count of Zollern
Frederick I, Burgrave of Nuremberg

Burkhard I, Count of Zollern (Latin: "Burchardus, Burcardus" ; born before 1025; killed as part of a feud in 1061) is considered the first well-documented ancestor of the Hohenzollern dynasty.
 Because of his name, it has been attempted to link the Hohenzollern family's descent to the medieval Burchardings family, but without success.
 His father may have been Friedrich, a count in the Sülichgau area (roughly corresponding to today's Tübingen district).
 His mother may have been Irmentrud, the daughter of Count Burkhard of Nellenburg.
The Northern Ice Field is near the summit of Mount Kilimanjaro in Tanzania, on the west slope of the peak.
 The Northern Ice Field and Eastern Ice Fields were connected to the Southern Ice Field and formed part of a continuous body of glacial ice atop Mount Kilimanjaro when first scientifically examined in 1912.
 By 1962 the Southern Ice Field separated from the Northern Ice Field and then by 1975 the Eastern Ice Field did as well.
 In 1912, the glaciated areas atop Mount Kilimanjaro covered 11.40 sqkm ; by 2011 this had been reduced to 1.76 sqkm , an 85 percent loss.
 At one time, ice flowing off the Northern Ice Field fed numerous glaciers, including, north to south, the Credner, Drygalski, Great Penck and Little Penck Glaciers.
Friedrich VII, Count of Zollern (d. after 6 October 1309) was a German nobleman.
 He was the ruling Count of Zollern from 1298 until his death.
Hohenzollern Castle (German:    ) is the ancestral seat of the imperial House of Hohenzollern.
 The third of three hilltop castles on the site, it is located atop Mount Hohenzollern, above and south of Hechingen, on the edge of the Swabian Jura of central Baden-Württemberg, Germany.
Conrad I of Nuremberg ( 1186 – 1261) was a Burgrave of Nuremberg of the House of Hohenzollern.
 He was the younger son of Frederick I of Nuremberg and Sophie of Raabs.
 His title as Count of Zollern was Conrad III, but Conrad I as Burgrave of Nuremberg.
Count Friedrich IV of Zollern (  1188 –  1255 ), also known as Burgrave Friedrich II of Nuremberg, was Burgrave of Nuremberg from 1204 to 1218 and Count of Zollern from 1218 until his death.
Friedrich II, Count von Zollern (died: 1142 or after 1145) was the eldest son of Friedrich I, Count of Zollern, and became Count of Zollern after his father's death around 1125.
Friedrich VI, Count of Zollern (died: 4 May 1298), also known as "Friedrich the Knight", or "Friedrich the Elder", was a Count of Hohenzollern
Friedrich V. of Zollern (died: 24 May 1289 at Hohenzollern Castle) nicknamed, "the Illustrious" was a Count of Zollern.
Friedrich I of Nuremberg (before 1139 – after 1 October 1200), the first Burgrave of Nuremberg from the House of Hohenzollern.
 He was the younger son of Count Friedrich II of Zollern, and became Count of Zollern as Friedrich III after the death of his other male relatives.