In his review of this disc by the Diogenes Quartet, the reviewer Richard Kraus says "The C minor fragment is an early work, begun and abandoned in 1820. Schubert apparently abandoned the sonata-form first movement at the end of the development."
As with most things musicological, this is disputable. Larius J. Ussi, in his very useful survey of Schubert's early quartets, says
"It is widely believed to be most of the first movement to a complete string quartet to which the last three movements have been lost. Even the last part of the first movement was missing by the time the manuscript came into the possession of the Gesellschaft der Musikfreunde of Vienna." (Franz Schubert's Unknown String Quartets - Part III (Chamber Music Journal 2004, vol.XV no.1))
In his survey, Ussi discusses the history of the manuscripts, especially in regard to those which are lost or come to us in fragmentary form. Quartet no.5 consists of the outer movements of a lost complete quartet. And some Schubert fans may remember that Quartet no.2 used to be a two-movement fragment (recorded that way by the Taneyev Quartet) until the rest of the work was discovered in a private collection.
For those interested, this survey of the early quartets can found online in the Chamber Music Journal's archive, in vol.14 no.3, vol.14 no.4 (for some reason a large 25 MB file) and vol.15 no.1.
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