The C-5R's engineering incorporated a live front axle, a configuration carried over from Kurtis Kraft Indianapolis monoposto racing cars at Briggs Cunningham's own suggestion. Suspension at both ends was by torsion bars. The lightweight aluminium body and spaceframe construction reflected an attempt to improve on the C-4R's performance envelope at Le Mans, and speed trap measurements confirmed the car was faster than the two factory C-4Rs also entered by the team. The C-5R's principal mechanical shortcoming was its drum brake system, which would become a central factor in its Le Mans campaign.
The C-5R made its racing debut at the 1953 24 Hours of Le Mans. Cunningham entered the car for long-standing works driver Phil Walters alongside John Fitch. Speed measurements at Les Hunaudieres — conducted formally for the first time that year — showed the C-5R reaching 249 km/h on the straight, making it the fastest sports car through that section of the circuit.
In the race itself, the C-5R ran competitively throughout. Only the factory C-Type Jaguars proved faster; Walters and Fitch finished third overall, behind the winning Jaguar of Tony Rolt and Duncan Hamilton and a second Jaguar driven by Stirling Moss and Peter Walters. After the race, Briggs Cunningham publicly attributed the defeat to the absence of disc brakes. The C-Type already carried the new braking technology, while the C-5R's drum brakes repeatedly overheated during the long straights and heavy braking zones at Le Mans, forcing the drivers to brake earlier than their competitors and costing lap time and race position.
At its next appearance, the 1953 12 Hours of Reims, the C-5R was badly damaged in an accident while John Fitch was at the wheel. The wrecked car was shipped back to the United States and rebuilt, but attempts to retrofit a disc brake system to the design failed. Cunningham subsequently redirected the team's development resources toward the new C-6R and filled out the race programme in the interim using OSCA and Ferrari machinery. The C-5R continued to compete in a small number of American sports car events before being sold to racing driver Charles Moran at the close of the 1953 season.
Although the C-5R contested only a handful of races, it occupies a significant place in Cunningham's programme. Its third-place finish at Le Mans in 1953 remains one of the strongest results the team achieved at the circuit, and the car's speed at Les Hunaudieres demonstrated that the Cunningham operation was genuinely capable of matching the best European sports car manufacturers on outright pace. The disc brake lesson absorbed at Le Mans shaped the direction of the subsequent C-6R development programme.