For most casual listeners, the words "Beethoven" and "sonata" almost always indicate one of the sonatas for solo piano, and with good reason; the piano sonatas comprise some of the greatest writing for piano in music history, and they are important listening for anyone. And if you happened to be a piano student of any skill, likewise your piano teacher eventually had you work on one of Beethoven's sonatas.
However, Beethoven didn't just write sonatas for piano alone. He also wrote sonatas for solo violin and piano, and for solo cello and piano.
Before turning to a specific sonata, it's interesting to look at the term itself. Sonata is an Italian term, which differentiates an intrumental work to be played rather than a vocal work to be sung (a cantata). Over time, especially in the Classical era when forms began to settle in to certain sets of expectations, a sonata became somewhat standardized as a large-scale work of three movements, which in turn were usually in a standardized sequence: an allegro which used a form in which a single melody (or maybe two) were stated, then developed, before being played again one final time before ending; a middle movement which was usually in a slower tempo; and a fast finale, often much faster than the first movement, and often in a Rondo form. The structure of the first movement--intro, theme, development, recapitulation, coda--became so entrenched that it in itself became known as sonata, or sonata-allegro, form. So important did sonata-allegro form become that it became the almost universal form in first movements of symphonies.
Of course, the history of the symphony is as complicated as that of the sonata, and as Classicism gave way to Romanticism and then to Modernism, adherences to standard forms came and went and came again. Even Beethoven was not always locked into the expected forms: he would start a three-movement piano sonata with a slow movement (the "Moonlight"), or he would write two- or four-movement sonatas. It is best, when thinking about musical forms and definitions of musical terms, that one remember the wise words of Captain Hector Barbossa of Pirates of the Caribbean fame: "The code is more what you'd call 'guidelines' than actual rules."
And when you're a towering genius like Beethoven, who is literally shaping the course of music history for centuries to come, well then...the guidelines are there to be ignored at will.
After all that, let's turn to Beethoven's Sonata for Cello and Piano No. 5 in D Major, which follows all the usual rules and adheres to the usual structure. Beethoven wrote this sonata at the same time as the one preceding it, the Sonata No. 4, in 1815 when his deafness was reaching its endpoint. He was entering what historians have called his "third period", which is when his most introspective and profound music seems to have resulted.
This sonata is apparently less frequently performed than the Sonata No. 3 (which as of this writing I have not heard), which I find interesting. The Fifth Sonata begins with a simple declarative statement by the piano, which sounds twice, seeming to hesitate after each sounding, before taking off into the initial allegro. The movement then propels through its formal demands before drawing to a close before the listener really expects. The second movement puts the cello's lyrical strengths on display, before a final movement that is fugal in nature. When the entire work ends, it is with a feeling of reflective abstraction as Beethoven, only left with his inner ear at this point, is transcribing sounds he can only imagine.
As much as I love the violin as a solo instrument, the cello is not to be slighted in its uses. The technical demands of the instrument are entirely different from those of the violin (which Beethoven had already mastered). Playing the cello has its own physical demands, and the instrument's voice resides in a much lower register, which means that it has to be treated differently than the violin if it is to be heard in full partnership with its accompanying instrument. Beethoven clearly understood the cello as well as he did the violin, judging by the results in this sonata.