His father was Count Conrad IV of Rietberg.
Conrad married before 1450 to Jacoba (d. 23 February 1492), a daughter of Count Gumprecht II of Neuenahr and Margaret of Limburg-Broich.
They had six children: Conrad V was buried in a section of the cloister of the former Cistercian Marienfeld Abbey which has not been preserved.
His grave stone contained a Latin text: In English translation: The grave stone of his wife also contained Latin text: In English translation: Conrad V built a chapel in the castle at Rietberg; it was consacreted on 2 July 1464.
In 1456, he had to give up his imperial immediacy and accept Rietberg as a fief from the Landgraviate of Hesse, in return for a compensation of 600 Rhenish guilders.