Why did Draupadi have five husbands?

Because of her ambition. Draupadi in her earlier life, was daughter of Nala and Damyanti and he wished that a number of qualities to be available in her husband. She did great penance to achieve the same and earned a boon from Lord Shiva. This was the reason why she had five husbands. read the full story here.

Draupadi in the court of Kauravas, where Yudhishthira lost her and his brothers