A bit off-topic in a house organ forum, but the five buttons are the register pulls. The instrument has a register in the lower half that can be played with more wind or (quieter) with less wind. Hence two pulls. In the treble it has two stops tuned to beat and the right pull opens only the main stop, the left both at the same time. In the middle there is a tremulant, but in the French harmoniums working with pressure wind it is always very violent and causes rather fast periodic interruptions of the tone. I don't know what this was used for in the past, but I think it sounds awful. Maybe it can be adjusted to make it sound smoother, but I've heard it on many such instruments, and it was never pleasant.
The organ builders in the early 19th century were fascinated by the possibility of using free-swinging reeds to make volume changes without deviations in pitch! Therefore several (even Cavaillé-Coll) constructed Harmoniums before the professions of organ- and harmonium-builder split up. And Harmonium stops were sometimes even built into large romantic organs as swell! If you look at it this way, the harmonium was the dominant form of the house organ between about 1850 and 1950, and is therefore not off-topic here.