1935, originally in reference to the Dionne babies, short for quintuplet "one of five" (children born at one birth).
Entries linking to quin
quintuplet n.
1873, "a set of five things" (originally in music), from quintuple (adj.) with ending from triplet. In plural, "five children born at one birth" it is recorded by 1889.
quint n.
mid-15c., quinte (late 13c. in Anglo-French), "a tax of one-fifth," from Old French quint, from Latin quintus "the fifth," ordinal to quinque "five" (from PIE root *penkwe- "five"). Used in English for "group or set of five" since 17c. First attested 1935 as a shortening of quintuplet (American English; British English prefers quin); used originally of the Dionne quintuplets, born May 28, 1934, near Callander, Ontario, Canada (compare quin).