He was the nephew of Francisco IV Fernández de la Cueva – Colonna, (* Barcelona, 1618/1619 – † Madrid (Palacio Real) 27 March 1676), 8th Duque de Alburquerque and many other lesser titles, also a Viceroy of New Spain, (1653–1660), and Viceroy of Sicily, (1667–1670), and the son of the 9th Duke of Alburquerque, and many other lesser titles, the cadet brother of the 8th Duke, and inheritor of the titles, Melchor Fernández de la Cueva (* Madrid, 2 March 1625 – † Madrid 12 October 1686).

Their first son, inheritor of the titles, was named Francisco VI Fernández de la Cueva (* Madrid 28 September 1692 – † Hortaleza, 23.

During his tenure as viceroy, Alburquerque significantly expanded New Spain's coast guard to counter piracy in the region.

During the War of the Spanish Succession, he directed the military of New Spain to prevent English and Dutch inroads into the Gulf Coast.

Alburquerque also confiscated the property owned by English and Dutch subjects in New Spain, using the proceeds from selling them to fund the Spanish war effort.

He demanded that New Spain's clergy turn over one tenth of their tithes to the colonial government, which Juan Ortega y Montañés strongly objected to.

[citation needed] In 1701 the Tribunal de la Acordada (literally, Court of Agreement) was founded.

Of those, 35,058 were freed, 888 were hanged, 1,729 were whipped; 19,410 were sentenced to prison for one or two years and 263 to labor on public works; 777 were banished to camps in the north, and the remainder were sent on to regular judges.

In spite of his faults, Fernández de la Cueva had a reputation as an affable, moderate and capable governor who maintained tranquility and security in the viceroyalty.