One of Mozart's friends was one Stadler, who was a fine musician.
Among other instruments, Stadler played the Clarinet, and it was for him that Mozart wrote two works with important parts for these instruments-a Concerto and this Quintet.
The Clarinet was just coming into use in Mozart's days, and he was very fond of it.
In the Quintet, written near the end of his life, he gives it a part more prominent than those allotted to the four Stringed instruments (two Violins, Viola and 'Cello). Perhaps that was done in order to let the clarinettist shine a little a 'star' performer.
The Quintet is in four Movements. which are respectively quick but suave, then slow and placid, next in dance style (the usual Minuet), and lastly debonair and dainty. This last Movement is an Air with five Variations.