Aegon V was the fifth king of his name to sit on the Iron Throne and the fifteenth king of the Targaryen dynasty to rule the Seven Kingdoms. He was the father of Jaehaerys II Targaryen, the grandfather of the Mad King Aerys II and his sister-wife Queen Rhaella, the great-grandfather of Rhaegar, Viserys, and Daenerys Targaryen, as well as great-grandfather of Robert, Stannis, and Renly Baratheon, and the younger brother of Maester Aemon Targaryen. In the books, he was dubbed "the Unlikely" because he was the fourth son of Maekar Targaryen, who was in turn the fourth son of Daeron II Targaryen, and thus Aegon was highly unlikely to inherit the crown.
Aegon, using the alias "Egg", spent many years traveling the Seven Kingdoms as a squire in the service of Ser Duncan the Tall, a hedge knight. At their first meeting Duncan was unaware of Egg's true identity, until he used his royal authority to save Duncan from being killed by his bullying older brother, Prince Aerion. Duncan was able to instead face Aerion on the tournament field and defeat him in combat. Unfortunately, Prince Baelor "Breakspear" Targaryen, the royal heir, was killed during the tournament. Prince Maekar - Aegon's father - despaired of Aerion's spoiled indolence and agreed to let Aegon serve as Duncan's squire to build character and gain experience of living in the "real" world.
Aegon ascended to the Iron Throne in 233 AL, following his father Maekar's death in battle with an outlaw lord. Of Aegon's three older brothers, Aerion had poisoned himself to death (by ill-advisedly drinking wildfire, thinking it might turn him into a dragon), Daeron had died of a pox and Aemon had disinherited himself by first joining the maesters and later the Night's Watch. As Aegon V Targaryen, he ruled for twenty-six years. During this time he made Ser Duncan the Lord Commander of the Kingsguard and secured an alliance between the Targaryens and House Baratheon by wedding his daughter Rhaelle to the then-Lord of Storm's End (she became the grandmother of Robert, Stannis and Renly Baratheon, giving the Baratheons their claim to the Iron Throne). He had three sons, Duncan (often called Duncan the Small), Jaehaerys, and Daeron, as well as his two daughters Shaera and Rhaelle.
Being the fourth son of a fourth son, Aegon V was known as "the Unlikely" because he was unlikely to have inherited the crown. Actually, given that two of his uncles had twin sons, Aegon was initially twelfth in line to the throne when he was born (during the reign of his grandfather Daeron II). Even after his father was crowned he was still fourth in line for many years.
Aegon V ruled wisely and well, but he had three major weaknesses. The first was that due to his years travelling across Westeros with Ser Duncan, he gained a great concern for the welfare of the Smallfolk, yet opinions about this varied. Commoners remember him as a great king who was genuinely concerned about their well-being, who ensured their economic livelihoods by raising taxes on aristocrats and wealthy merchants, and who punished lords who abused the rights of the commoners they ruled over. The nobility of the Seven Kingdoms, meanwhile, grew to resent Aegon V - for exactly the same reasons.
Second, Aegon V indulged his sons: having married for love himself, he permitted his sons to do the same, although this was not politically wise and made him enemies within the Seven Kingdoms. The nobility was already growing to resent him for his liberal policies with the smallfolk, and a marriage-alliance with one of the Great Houses would have helped to stabilize Targaryen rule. Duncan the Small famously abdicated his place in the line of succession to marry a commoner, Jenny of Oldstones (a story which has become a favorite theme of romantic songs, which gave Sansa Stark an idealized vision of courtly love). Shaera was supposed to marry Luthor Tyrell, Jaehaerys was supposed to marry a Tully girl, and Daeron was supposed to marry the young Olenna Redwyne. Aegon V was determined to put an end to the incestuous marriage practices of the Targaryens but this only seemed to encourage a forbidden romance between Jaehaerys and Shaera, who eloped and married without his permission. Daeron, a splendid and brave knight, did not want to marry Olenna either - and is heavily implied to be homosexual in The World of Ice and Fire. Thus after his two older brothers broke their betrothals he broke his as well, saying that his father could not rightfully force him marry against his will when he had already relented for his two elder brothers. Olenna Redwyne was then free to marry Lord Luthor, becoming Olenna Tyrell.
Third, Aegon V also had an overwhelming obsession with hatching the surviving Targaryen dragon eggs. He encountered so much resistance from the Great Houses over the years trying to enact reforms that would benefit the smallfolk that he came to believe that the only way to bring them all in line again was to enforce royal power with new dragons. These last two weaknesses culminated in 259 AL at the so-called "Tragedy at Summerhall". This was a fire that got out of control and destroyed the castle, killing Aegon V, Ser Duncan the Tall, and Prince Duncan the Small. On the same night, Aegon's great-grandson Rhaegar Targaryen was born. Aegon V was succeeded by his son Jaehaerys II.
- In TV series, Jaehaerys II was completely omitted from the lore of TV series while Jon Snow was comfirmed to be Rhaegar's son, and those both made Aegon V the father of the Mad King and his sister-wife Queen Rhaella, the grandfather of Rhaegar, Viserys and Daenerys, and the great-grandfather of Jon Snow.