The car began life as the Hesketh 308C, designed by Harvey Postlethwaite for Hesketh Racing in 1975. The 308C featured rubber suspension, a concept Postlethwaite had pioneered on the preceding 308B, and was powered by the Ford-Cosworth DFV. It debuted at the 1975 Italian Grand Prix in the hands of James Hunt, who finished fifth, and Hunt placed fourth in the United States Grand Prix at season's end.
Before the 1976 season, Canadian oil millionaire Walter Wolf purchased 60 percent of Frank Williams Racing Cars, transforming the team into Wolf–Williams Racing. Wolf simultaneously bought the assets of Hesketh Racing, which had recently withdrawn from Formula One. The Hesketh 308C was rebranded as the Wolf–Williams FW05, while the older Williams FW04 was similarly rebadged as the Wolf–Williams FW04. Postlethwaite joined the restructured team as chief engineer. The team was based at the Williams facility in Reading but used much of the equipment and cars formerly belonging to Hesketh Racing. One noted drawback that emerged through the season was that the FW05 proved to be overweight.
The FW05 was introduced at the Brazilian Grand Prix, driven by Belgian veteran Jacky Ickx. At that opening race, Ickx was outqualified by teammate Renzo Zorzi in the older FW04 and finished eighth, with Zorzi ninth. After Brazil, Wolf–Williams took delivery of a second FW05, making the FW04 redundant.
The team ran two drivers through the first half of the season: Ickx and French driver Michel Leclère, who replaced Zorzi when the Italian's sponsorship funds ran out. Results were modest. Both cars failed to qualify at the United States Grand Prix West, where the field was limited to twenty starters on safety grounds. In South Africa, both finished — Leclère thirteenth, Ickx sixteenth. At the Belgian Grand Prix, Ickx failed to qualify while Leclère started and finished eleventh. For the Swedish Grand Prix, only one car was entered as Ickx was competing in the 24 Hours of Le Mans, which he won with Gijs van Lennep in a Porsche 936.
For the British Grand Prix, Leclère departed and the team ran a single car for Ickx. He failed to qualify, and was fired after the race. Arturo Merzario replaced him for the second half of the season. At the German Grand Prix, Merzario stopped voluntarily after witnessing Niki Lauda's severe accident at the Nürburgring and was among the drivers who dragged Lauda from his burning Ferrari. He managed to return for the restart but retired with brake failure on lap three. Further retirements followed in Austria and the Netherlands.
At the Italian Grand Prix, a complex qualifying situation involving disqualified lap times for Hunt, Jochen Mass, and John Watson shuffled the grid and allowed Merzario to take a place he had initially not held. Merzario later withdrew due to brake problems. For the Canadian Grand Prix, New Zealander Chris Amon joined the team in a second car but was struck by another car after a spin and chose not to race. Warwick Brown replaced Amon for the United States Grand Prix East, finishing fourteenth. For the final race in Japan, a last-minute sponsorship withdrawal led Frank Williams to replace local driver Masami Kuwashima with Austrian Hans Binder, who was allowed to start with the consent of other teams. Both Merzario and Binder retired.
At the end of 1976, Walter Wolf restructured the team and removed Frank Williams from the managerial role. Williams, disillusioned, left the team entirely and, together with Patrick Head, founded Williams Grand Prix Engineering in 1977. Wolf subsequently bought the remaining 40 percent share from Williams and the team became Walter Wolf Racing, continuing with Postlethwaite's technical direction.
The FW05's single season encapsulates a transitional and difficult period in early Williams history. Although it produced no victories, it was the car that bore the Williams name during the crucial months when the team's founder was effectively pushed out of his own outfit. The episode provided the spur for Williams and Head to build the independent team that would eventually become one of Formula One's dominant forces. The car itself, derived from the Postlethwaite-designed Hesketh 308C, illustrated how closely intertwined the small British constructors of the mid-1970s were in terms of people, ideas, and machinery.