Gerald FitzGerald, 3rd Earl of Desmond
Gerald FitzMaurice FitzGerald( 1335 – 1398), also known by the Irish Gaelic" Gearóid Iarla"( Earl Gerald), was the 3rd Earl of Desmond, in southwestern Ireland, under the first creation of that title, and a member of the Hiberno- Norman dynasty of the FitzGerald, or Geraldines.
He was the son of Maurice FitzGerald, 1st Earl of Desmond, by his third wife Aveline( Eleanor), daughter of Nicholas FitzMaurice, 3rd Lord of Kerry.
He was half- brother to Maurice FitzGerald, 2nd Earl of Desmond.
Maurice Fitzgerald, 2nd Earl of Desmond, would have been followed by Gerald's older brother, Nicholas, but Nicholas was described as" an idiot", and so was passed over for the earldom.
Because of this, some older histories list Gerald as the 4th Earl.
John FitzGerald, de facto 12th Earl of Desmond
John FitzGerald, de facto 12th Earl of Desmond( died December 1536) was the brother of Thomas FitzGerald, 11th Earl of Desmond.
Upon his brother's death in 1534, John disputed the title to the earldom of his brother's grandson, James FitzGerald, de jure 12th Earl of Desmond.
According to the" Annals of the Four Masters", John FitzThomas FitzGerald was believed to have instigated the murder of his older brother, James FitzGerald, 8th Earl of Desmond in 1487, and had been expelled by his brother Maurice FitzGerald, 9th Earl of Desmond.
< ref>[ https://books.google.com/books?id=DdhC3eVIdHgC&pg=PA530&dq=James+FitzGerald,+8th+Earl+of+Desmond&hl=en&sa=X&ved=0ahUKEwjDkbTshJjZAhVPrVkKHVoGDLc4FBDoAQg_MAQ#v=onepage&q=
James FitzGerald, 8th Earl of Desmond&f= false Connellan, Owen.
" The Annals of Ireland[ from A.D. 1171 to A.D. 1616", Dublin.
Brian Geraghty, 1846, p. 309]
James FitzGerald, 6th Earl of Desmond
James FitzGerald, 6th Earl of Desmond( d. 1462), called' the Usurper', was the youngest son of Gerald FitzGerald, 3rd Earl of Desmond, and Lady Eleanor, daughter of James Butler, 2nd Earl of Ormond.
Gerald FitzGerald, 5th Earl of Kildare
Gerald FitzMaurice FitzGerald, 5th Earl of Kildare( d. before 24 June 1428) was an Irish peer.
Gerald was the son of Maurice FitzGerald, 4th Earl of Kildare and Elizabeth Burghersh.
John FitzGerald, 4th Earl of Desmond
John FitzGerald, 4th Earl of Desmond (died 1399) was the son of Gerald FitzGerald, 3rd Earl of Desmond.
He married and had one son, Thomas, who succeeded him as Earl of Desmond.
According to Burke, John FitzGerald married Joan Roche, the daughter of Lord Fermoy.
In March 1399 FitzGerald drowned at Ardfinnan on the River Suir, and was buried at Youghal.
He was succeeded by his son Thomas FitzJohn FitzGerald, 5th Earl of Desmond.
Thomas FitzGerald, 5th Earl of Desmond
Thomas FitzGerald, 5th Earl of Desmond (c. 1386–1420), was the only son of John FitzGerald, 4th Earl of Desmond.
Upon John's death in 1399, Thomas succeeded to the earldom of Desmond, which lay in Munster, in the southwest of Ireland.
In 1418, Thomas was dispossessed of his lands and deprived of his earldom by his paternal uncle, James FitzGerald, 6th Earl of Desmond, after Thomas had concluded a marriage far below his station to Catherine MacCormac of Abbeyfeale; Catherine was the daughter one of Thomas's dependants, William MacCormac, known as "the Monk of Feale.
"
A marriage between a man of Norman blood and a woman of Gaelic ancestry was in violation of the Statutes of Kilkenny.
This ill-fated romance was the subject of the air "Desmond's Song" by the Irish poet Thomas Moore.
After the loss of his earldom, Thomas withdrew to France, where he "died at Rouen, 10th August 1420, and was buried at Paris 'with great and mighty show, where the two kings of England and France were present.'"
James FitzGerald, 8th Earl of Desmond
James FitzGerald, 8th Earl of Desmond( 1459 – 1487) was the son of Thomas FitzGerald, 7th Earl of Desmond and his wife, Ellice de Barry, daughter of William Barry, 8th Baron Barry, and Ellen de la Roche.
Maurice FitzGerald, 9th Earl of Desmond
Maurice FitzGerald, 9th Earl of Desmond( died 1520) was the brother of James FitzGerald, 8th Earl of Desmond.
James FitzThomas FitzGerald
James FitzThomas FitzGerald, the Súgán Earl of Desmond( d. 1608), was the eldest son of Sir Thomas Fitzgerald, commonly called" Thomas RoeTomás Ruadh" or" Red Thomas."
Maurice FitzGerald, 2nd Earl of Desmond
Maurice FitzMaurice FitzGerald, 2nd Earl of Desmond( d. 1358)( Maurice Óg) was the son of Maurice FitzGerald, 1st Earl of Desmond, and his first wife, Catherine de Burgh.
( Some sources list her as Margaret.)
The 2nd Earl married Beatrice de Stafford, daughter of Ralph de Stafford, 1st Earl of Stafford and Margaret Audley, but died without any male issue, and was therefore succeeded in the Earldom of Desmond by his half- brother Gerald FitzGerald, 3rd Earl of Desmond.
FitzGerald's widow married
Thomas de Ros, 4th Baron de Ros around a year after FitzGerald's death.

Question: Who is the paternal grandfather of Thomas Fitzgerald, 5Th Earl Of Desmond?
Answer: Gerald FitzGerald, 3rd Earl of Desmond