An Atlanta woman came forward in an interview broadcast Monday night with details about what she called a 13-year affair with Herman Cain, the Republican presidential contender whose campaign was already struggling to overcome damage from accusations of sexual harassment. The woman, Ginger White, made the disclosure in an interview with Fox 5 News in Atlanta, becoming the fifth person to accuse Mr. Cain of improper behavior. Ms. White is not, however, claiming that harassment took place. Rather, she described what amounted, in her words, to a romance.