My partner started cocp on day 1 of her period, but the bleeding stopped a few hours later. would she still have been protected within the first 5 day?

Don't worry: Starting COCPs on the first day of the menstrual cycle confers the maximum contraceptive benefit, and you don't need to worry about using a backup method of contraception. Many women get some irregular vaginal spotting/bleeding when they start using contraceptive pills. It often takes 3 cycles of pills to become regular. For more info: www.askyourgynecologist.org.