I stay at a hostel in Tsim Sha Tsui, near the MTR station. I need to be at the airport at 5 AM.

First of all, you'd better to arrive at the airport 2 hours in advance. Thus you are advised to take bus no.N21 from Haiphong Road, Nathan Road and arrive at Passenger Terminal Building, Cheong Tat Road directly. The duration is about 80 mins. It costs 23 HKD per person.