The 1956/7 500 TRC was an altered version of the successful 500 TR of the previous year.The most significant changes were made to comply with Annex C of the International Racing Code, resulting in the "C" added to the model's name. In order to follow these regulations, Ferrari widened the cockpit, added a passenger side door, fitted a full width windscreen with wipers, installed a 120 liters (32 U.S. gal) fuel tank and even added a stowable convertible top. The Scaglietti-built body, while similar to that of the 500 TR, had a lower hood and slightly reshaped wheel arches and fenders. Another change from the 500 TR was the longer 2,350 mm (93 in) wheelbase, derived from the 860 Monza. Suspension featured coil springs all around with a live rear axle. Like the 500 TR, the car weighed only 680 kg (1,500 lb), and produced 180 hp (132 kW). Ferrari manufactured a total of 19 500 TRC chassis between 1956 and 1957. This model was the last 4-cylinder racing car built by Ferrari.
Even though this model was never raced by Scuderia Ferrari as a works car, 500 TRCs were successfully raced by independent teams and drivers. At the 1957 24 Hours of Le Mans, a 500 TRC finished 7th overall, claiming victory in the 2,000 cc class, .Another 500 TRC claimed a 2,000 cc class win at the 1958 Targa Florio.
Two 500 TRC chassis were upgraded by factory to 2.5-litre specification, creating the very rare 625 TRC model. They were both owned and raced by John von Neumann, owner of the Ferrari Representatives of California dealership. S/n 0672MDTR was further fitted with the 3.4 L 860 Monza engine, just to be refitted once more in 1958, this time with a 3.0 L 250 Testa Rossa unit. S/n 0680MDTR was sold on May 12, 2012 at RM Sotheby's auction in Monaco for €5 million.