Cut each chicken breast in half on the diagonal to get 4 portions about equal in weight. (Two will be smaller but thicker, the other two larger, but thinner). Sprinkle the chicken with the five spice powder and salt.
Place 3 tablespoons flour in a shallow dish. Dredge both sides of the chicken in the flour.
Heat the oil in a large skillet over medium heat. Add the chicken, skinned-side down, and cook until brown on the bottom, about 6 minutes. Remove from the heat and transfer the chicken, skinned-side up, to a baking sheet. Bake until an instant read thermometer inserted into the thickest part of the breast registers 165°, 15 to 20 minutes.
Return the skillet to medium heat, add shallot and cook, stirring, until fragrant, about 1 minute. Add the sherry and cranberries; cook until the sherry is reduced by about half and the cranberries are beginning to soften, about 1 minute. Add 1 cup broth; brink to a boil and cook, stirring occasionally, until the cranberries are very soft, about 3 minutes more.