Canada, whose National Olympic Committee has agreed to fund the challenge, has joined with England, Scotland, Australia and New Zealand in making the protest in Lausanne.
The International Badminton Federation (IBF) this year imposed a 3x15 format (best of three sets, first to 15 points) for men's singles and doubles but made all women's and mixed doubles 3x11.
The IBF has, however, agreed to reconsider at its council meeting in Bangkok last month following objections.
Its council, however, subsequently refused to make any changes to the two-tier system, which had itself replaced a year-long experimental flirtation with seven-point games to try to increase the sport's appeal.
The 5x7 system had been seen by its advocates as providing more key points, greater excitement -
The European Badminton Union has described the latest scoring system as "an attack on the women's game". The challenge to CAS, however, questions the legitimacy of the IBF to impose a new rule without it having been proposed by a member nation.
"We don't believe we can accept the right to make this decision because it came out of the blue," said Ian Moss, the chief executive of Badminton Canada.
"The council is supposed to deal with what's on the table, not come up with something new. As a result, it has come up with something which in the western world discriminates against women."
If the protest is successful, the five nations will use the authority of the court's decision to apply moral pressure to the IBF.
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