In lang=en terms the difference between quintuplet and quintet

is that quintuplet is a tuplet of five notes to be played in the time for four while quintet is a group of five musicians, fit to play such a piece of music together.

As nouns the difference between quintuplet and quintet

is that quintuplet is one of a group of five babies born from the same mother during the same birth while quintet is a composition (a type of chamber music) in five parts (typically each a singer or instrumentalist, sometimes several musicians.