In five days of talks here, a top-level United Nations delegation has failed to get South Africa agreement on a date to launch a Western-designed peace settlement to bring the Pretoria-run territory of Namibia (Southwest Africa) to independence.

Efforts of the U.N. negotiators are now centered on gaining South Africa approval of a compromise that could be regarded as "a significant and honest piece of progress," toward implementation of the plan, according to high-level source involved in the talks.

To meet that criteria, South Africa must move toward acceptance of a time frame for implementing the plan, according to the source.

"We're still holding our breath," said one Western official informed on the talks.

Without such "progress," the United States and four of its allies who have been architects of the peace settlement between Pretoria and its guerrilla foes, the Southwest Africa People's Organization (SWAPO), will have little to offer to the U.N. General Assembly. The assembly is expected to demand that the Security Council take punitive action against South Africa, possibly some kind of transportation or economic sanctions.

The U.N. mission here is an attempt to overcome South African reluctance to set in motion the settlement that both it and SWAPO accepted in July 1978. Since then, there have been discussions to meet South African concerns about how the cease-fire and subsequent universal suffrage elections would be run by the U.N. and its proposed 10,000-member military task force.

This week's talks have bogged down over South Africa's refusal to agree to a specific date for a cease-fire until the United Nations publicly takes steps to cut off the political and financial aid it has been giving SWAPO for more than a decade.

The South Africans say this aid, which they claim amounts to between $10 million and $15 million annually in direct and indirect help, impugns the international organization's impartiality and therefore its ability to oversee the elections in an unbiased manner.

The U.N. position is that any moves to stop its assistance for SWAPO should be made as implementation of the plan commences and therefore, South Africa must first agree to a date for that.