I agree with Annie about the sleeping ...it could be growing pains and as she has a cough it could be flu, keep an eye on her and have her checked out has she had any fevers /chills?
7-8 hours of sleep a night is not near enough for a 5-year-old. She should be getting 11 hours a night; some kids even sleep 12. No wonder she's tired. I'd complain of aches and pains too, if I were sleep deprived. Try getting her a whole lot more sleep, put her to bed by 8 pm at the latest and don't wake her until 7 am if your schedule allows. If she must get up earlier, put her to bed earlier. See if that helps.