Mithradates V was a relative of the Parthian king Osroes I, who had inherited, when his father Pacorus II had died in 105 CE, both the empire and a civil war against Vologases III, ruler of the eastern part of what once had been one state. Worse, Osroes had to face a Roman invasion (114) and the temporary loss of large territories in the west. When the Roman commander, the emperor Trajan, died in 117, his successor Hadrian abandoned the Roman conquests, but Osroes could not recover all lost territories. Armenia, for example, became part of the realm of the rebel Vologases III, and it seems that Characene in the south had become independent too.
Mithradates had fought against the Romans and appears to have been a co-ruler of Osroes, whom he succeeded in 115. His own coins were minted at Ecbatana, while Vologases continued to be in control of the eastern part of the empire. From coins, we can deduce that there briefly was another, unidentified king in about 140.
In c.147, Mithradates V and Vologases III were succeeded by Vologases IV, who was a son of Mithradates V.
The chronology of the Arsacid kings of the Parthian Empire is less well-understood than, for example, the sequence of Seleucid and Ptolemaic kings or the emperors of Rome. This information is based on the researches by G.R.F. Assar, as published in "Iran under the Arsakids, 247 BC – AD 224/227" in: Numismatic Art of Persia (2011).