This remarkable work was the first of Mozart's string quintets, a group of works completed only in his final years with the composition of the four great quintets of 1787 to 1791 (a fifth, K. 406 [516b], is an arrangement of the Wind Serenade in C minor, K. 388). At the time of its composition in 1773, the quintet for two violins, two violas, and cello was a little-explored genre, composers such as Boccherini preferring the alternative disposition of two cellos rather than two violas. It was originally composed in Salzburg in the spring of 1773 in the aftermath of the Mozarts' (Wolfgang and his father Leopold) return from their third and final visit to Italy. Its immediate inspiration appears to have been two string quintets by Michael Haydn, the younger brother of the famous Joseph Haydn. Michael Haydn, who held the post of Konzertmeister (concertmaster) at the court of the Archbishop of Salzburg from 1763, composed a number of string quintets which he styled "notturni," a designation generally applied during this period to works of a lighter, serenade-like character.

Although Mozart's quintet displays some signs of the direct influence of Haydn's works (a duet for violin and viola in the second of the four movements), it is a far more ambitious and experimental work, displaying signs of immaturity only in the limited scope of the writing for the second viola. The four movements are marked Allegro moderato, Adagio, Menuetto, and Allegro. The first has a quasi-symphonic feel to it, with a particularly strong development section, while the final movement provides an early example of the contrapuntal skills Mozart would hone so finely in later years. Only in the inner movements is there evidence of the notturno-like style, with suggestions of echo-effects implied in the Adagio, explicit in the trio section of the Menuetto.

In the December of the same year Mozart made revisions to the work, the most substantial of which involved a complete rewriting of the extensive and complex finale. These were apparently made after Mozart had heard Joseph Haydn's Opp. 17 and 20 string quartets during a visit to Vienna in July and August 1773. Mozart himself obviously thought highly enough of the quintet for it to be one of a selected group of works he took with him on the long journey to Mannheim and Paris four years; a letter to his father from Mannheim states that it was one of the works he had copied and left there before resuming the journey to Paris.

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