Grandson of Herod & Mariamne
Son of Alexander & Glaphyra

Herod himself arranged the marriage of his oldest Hasmonean son (Alexander) to the daughter of Archelaus of Cappadocia but returned her to her father soon after her husband's execution (7 BCE), while retaining custody of her children. So Tigranes, though named for his mother's illustrious Armenian ancestor, was reared as a Jew. Yet, after Herod died (4 BCE), Tigranes & his brother rejoined their mother in their maternal grandfather's court & renounced their paternal Jewish heritage.

Ten years later, when Rome's client king of Armenia was murdered by his own subjects, Augustus ordered Tiberius to install Tigranes as his successor. The Armenian nobles, however, forced Tigranes to accept their former queen Erato (a descendant of Antiochus III) as his co-ruler. While no record of their joint reign has survived apart from coins, this arrangement must not have worked out for long, since both Tigranes & Erato were deposed in 12 CE. Still Tigranes did not renounce his claim to the throne of Armenia. For when his successor died (18 CE), Tigranes' maternal grandfather (Archelaus) tried unsuccessfully to reinstate him. Some time after this he must have gone to Rome. For unspecified charges were made against him during Tiberius' reign of terror in 36 CE, which he apparently did not survive.

References: Josephus, Antiquities 18.140. 
                   _____, War 1.552-554.
                   Augustus, Res Gestae 26.
                   Tacitus, Annals 6.40.

Other online resources:

• Tigranes V of Armenia - article in Wikipedia's web.