In 1784, buoyed by his popularity in Vienna, Mozart composed six piano concertos. This fifth piano concerto was composed on September 30 for the blind female pianist Maria Theresia von Paradis. A student of Salieri, she was a musician who skillfully played the piano and also composed. It is believed that she met Mozart in Salzburg in 1783 and commissioned the work for her European tour.

Mozart himself performed this concerto in February of the following year. Upon hearing it, his father Leopold wrote to Mozart's sister Nannerl that he "shed tears of joy" at the rich instrumentation. The letter also noted that the Emperor himself exclaimed "Bravo, Mozart," praising it highly, which clearly indicates the concert's enthusiastic reception.

The composer's own cadenzas include three for the first movement, two for the third movement, and one Eingang (lead-in) for the third movement.

Movements

• First Movement: Allegro vivace, B-flat major, 4/4 time. Concerto-sonata form. A movement filled with joyful brightness. The piano's prominent features include movements utilizing scales and arpeggios.
• Second Movement: Andante un poco sostenuto, G minor, 2/4 time. Variation form. Consists of a theme and five variations. This movement possesses the unique beauty and forward momentum characteristic of Mozart's minor keys.
• Third Movement: Allegro vivace, B-flat major, 6/8 time. Rondo form. In stark contrast to the previous movement, this is a bright and brilliant finale. Nevertheless, it includes a fierce section in B minor midway, revealing shades of contrast.