Cary was a younger son of Robert Dillon, 2nd Earl of Roscommon (died 1642), by his third wife Anne Strode, daughter of Sir William Strode of Somerset. His mother, who died about 1650, was the widow of Henry Folliott, 1st Baron Folliott, by whom she had several children. As a younger son with his livelihood to earn in the war-torn Ireland of the 1640s and 1650s, a military career was an obvious choice for him: he was made a Captain by the age of seventeen. Although Samuel Pepys in the Great Diary always called him "Colonel Dillon" he was apparently only a Lieutenant until 1684, when he became a Major, and subsequently a Colonel.
His father in the 1630s had been a supporter of Thomas Wentworth, 1st Earl of Strafford, the formidable and , for a time, virtually all-powerful Lord Deputy of Ireland, as was his half-brother James Dillon, 3rd Earl of Roscommon, and a family tie between the Dillons and the Wentworths was created when James married Strafford's sister Elizabeth. During the English Civil War, both the Dillon brothers were staunch Royalists: James, who died in 1649, was posthumously listed in the Act for the Settlement of Ireland 1652 as one of the ten leaders of the Royalist cause in Ireland who were excluded from pardon, and thus liable to forfeiture of their estates.
Following the Restoration of Charles II, Dillon entered politics, sitting in the Irish House of Commons as MP for Banagher in the Parliament of 1661-1666. His career was almost ruined in 1662 when he acted as second to Colonel Thomas Howard in his notorious duel with Henry Jermyn, 1st Baron Dover (Howard and Dover being rivals for the affections of the notoriously promiscuous Anna Talbot, Countess of Shrewsbury). Howard left Lord Dover for dead, and Dillon killed Dover's second, Giles Rawlings. He and Howard initially fled, but later returned to stand their trials. As was usual in an affair of honour, they were both acquitted, as killing a man in a duel was then generally regarded as an act of self-defence.
This check to his career was temporary, and after 1670 his rise in Irish public life was rapid. He was sworn a member of the Privy Council of Ireland in 1673, and also became Master of the Irish Mint, Commissary-General of the Horse of Ireland, Surveyor-General for Customs and Excise in Ireland, and a Governor of the Royal Hospital Kilmainham. In 1685, on the death of his nephew, the poet Wentworth Dillon, 4th Earl of Roscommon, he succeeded to the Earldom. The following year he clashed bitterly with the Duke of Tyrconnel, the rising Roman Catholic Royal favourite. Tyrconnel, as Lieutenant-General of the Irish Army, had removed all the Protestant officers of the regiment which was stationed at Kilkenny. Roscommon, with it seems considerable justification, challenged his legal right to do so, and when the matter came before the Lord Lieutenant of Ireland, Lord Clarendon, Roscommon called Tyrconnel a liar to his face: this was a shrewd blow, since Tyrconnel had the unfortunate nickname "Lying Dick Talbot". The "Kilkenny affair" caused something of a furore at home, but did not damage Tyrconnel's standing at the English Court.
Having served the Stuart dynasty with notable loyalty both during the Civil War and after the Restoration, Lord Roscommon, like many of the Irish Protestant ruling class, changed sides after the downfall and flight to France of James II in 1688. Roscommon and the majority of his fellow peers were opposed to James's pro-Catholic policy, and appalled at the mishandling of the economy by Tyrconnel, the Lord Deputy of Ireland, with whom Roscommon had a bitter personal feud as well. When James in 1689 attempted to reconquer England by occupying Ireland, Roscommon offered his services to King William III of England. He was commissioned to raise troops on William's behalf, and was present at the taking of Carrickfergus, the crucial first step in William's campaign to wrest control of Ireland from James's invading army, in August 1689. In consequence he was attainted for treason by King James II's Patriot Parliament held in Dublin in the summer of 1689. He died the following November.
He married Katherine Werden (died 1683), daughter of John Werden of Chester, by whom he had a son and heir, Robert Dillon, 6th Earl of Roscommon (died 1715), who is said still to have been a young child when his father died. The 5th Earl also had two daughters, Anne, who married Sir Thomas Nugent in about 1675, and Catherine (died 1674), who married Hugh Montgomery, 2nd Earl of Mount Alexander. The sisters were so many years older than their brother that it is possible they were children of an earlier unrecorded marriage. If so their mother must have died before 1660, since it is clear from the Diary of Samuel Pepys that Dillon was free to marry between 1660 and 1668.
Pepys evidently liked "Colonel Dillon", whom he first seems to have met in 1660, when he called him "a very merry and witty companion". At the start of the Diary period (1660-1669) one of Pepys's closest friends was a young clergyman called Butler (nicknamed "Monsieur l'Impertinent", apparently because he never stopped talking), who was probably, like Dillon, an Irishman. Pepys admired both of Butler's sisters, especially Frances (nicknamed "la belle Boteler"), whom he thought one of the greatest beauties in London. Dillon courted Frances, and matters proceeded as far as an engagement, but this was broken off in 1662, apparently after a violent quarrel between Dillon and Frances's brother "Monsiuer l'Impertinent", who complained of Dillon's "knavery" to him. In the summer of 1668 Dillon apparently renewed his proposal of marriage- Pepys saw him and Frances riding in a carriage together- but it seems that Frances declined the offer. It is not known whether Frances ever married.