Yes, it is a string quartet, and was written in g minor, and by Mozart.

A string quintet has five string instruments, either as 2 violins, 2 violas and one violoncello (as the Mozart string quintets, K. 174, K. 515, K. 516, K. 516b (406), K. 593 & K. 614 or Brahms' 2 string quintets, op. 88 & op. 111) or as 2 violins, one viola and 2 violoncellos (as the numerous Boccherini string quintets). However there is another category with a standard string quartet and a double bass, sometimes referred to as a string quintet.

The string quintet played beautifully all evening.

In brief, a string quartet is accompanied with a piano. A string quintet has two violins, a viola and a cello.

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