CREATE TABLE table_5889 ("Year" FLOAT, "Men's singles" TEXT, "Women's singles" TEXT, "Men's doubles" TEXT, "Women's doubles" TEXT, "Mixed doubles" TEXT)

Women's singles of astrid eidenbenz, and a Men's doubles of no competition is part of mixed doubles?
SELECT "Mixed doubles" FROM table_5889 WHERE "Women's singles" = 'astrid eidenbenz' AND "Men's doubles" = 'no competition'
SELECT "Mixed doubles" FROM "table_5889" WHERE "Men's doubles" = 'no competition' AND "Women's singles" = 'astrid eidenbenz'