If my baby is 5month 3weeks, can he starts to drink 6 month old formula? What's the different between the first six month and after six month formula?

No problem. There is usually a reasonable amount of wiggle room in such things and i doubt 1 week will make a difference. Some formulas differ in their fat and caloric content for different ages to accomodate different nutritional needs in a growing infant. At 6 months, with the guidance of your doctor, you can also start "solids" (ie: jar baby food , baby cereal, or homemade purees).