Iacopo V's paternal grandfather was Jacopo III, the 3rd lord of Piombino and Battistini Kampofregozo and of the daughter of Doge of Genoa Jano I.
His maternal grandfather was Antonio, the 1st Duke of Amalfi from Todeschini-Piccolomini, and of Princess Mary d'Aragona, illegitimate daughter of the Ferdinand the Ist, the King of Naples.
[1] Like his predecessors, he initially allied with the Aragonese of Naples, in his case by marrying Marianna of Aragon in 1510, widow of Roberto II Sanseverino.
After Marianna's death, he married three granddaughters of Lorenzo de' Medici and nieces of Pope Leo X: Emilia Ridolfi (daughter of Contessina de' Medici); she died soon afterwards, and Jacopo remarried to her younger sister Clarice.
After her death, he married a fourth time to Elena Salviati, daughter of Lucrezia de' Medici.