Heat 2 tablespoons of the oil in a large skillet over medium-high heat. Season the chicken with the cumin, ½ teaspoon salt, and ¼ teaspoon black pepper. In batches, cook the chicken until golden brown and cooked through, about 2 minutes per side. Cut into strips.
In a small bowl, whisk together the lime juice, red pepper, the remaining 3 tablespoons of oil, and ½ teaspoon salt.
In a large bowl, toss the chicken, spinach, cilantro, carrots, and raisins with the dressing.