After the Swiss Federal Railways (SBB) took over the Gotthard Line in 1909, it quickly became apparent that locomotives had to be acquired with greater performance in order to make operations on the steep grades on the Gotthard and the approach lines on flat territory more efficient. In addition to serving as motive power for freight locomotives, these locomotives also had to be capable of pulling express trains on the steep grades, which required a maximum speed of 65 km/h / 41 mph in addition to high pulling power.
The two prototypes, road numbers 2901 and 2902, of the class C 5/6 were available for testing as early as 1913. They were equipped with four-cylinder running gear and simple expansion, which did not turn out particularly well. On the regular production locomotives, recourse was therefore made to the good experience with the running gear for the C 4/5 locomotives in the series 2701–32 and four-cylinder compound running gear based on Von-Borries was installed. In this instance, the two inboard high-pressure cylinders drove the second driving wheel set, and the outboard low-pressure cylinders drove the third driving wheel set. The rear coupled wheel set had 25 mm / 1 inch side play and the treads on the center wheel set were made narrower to ensure good running on curves. Between 1913 and 1917, 28 regular production units were placed into service with the road numbers 2951-2978, whereby road number 2978 was also the last standard gauge steam locomotive delivered to the SBB.
However as early as 1921, these units (immediately designated as "Elephants") became superfluous with the complete electrification of the Gotthard Line, and they were transferred to flat territory as well as to large switchyards. There they survived even with partially forced use on the DRG and after the end of the war on the SNCF well into the Fifties, when the first units were placed in storage. At least the steam era on the SBB ended befitting the status of these locomotives because the last C 5/6 built, road number 2978, took the last official SBB steam train on November 30, 1968 to Winterthur.
Just four "Elephants" remain preserved: The Swiss Transportation Museum in Lucerne houses road number C 5/6 2965. It was displayed until 1982 as a memorial in Erstfeld. Road number 2969 is being overhauled by Eurovapor (locomotive maintenance facility in Sulgen), whereby road number 2958 is functioning as a source of spare parts. Road number 2978 of SBB Historic is still operational and is stored at Delémont.