Assuming you have a US passport, Timatic says of entry requirements into Hong Kong:

"Passports and other documents accepted for entry must be valid for a minimum of 1 month beyond the period of intended stay."

I take that as meaning that at the most, you need 4 months validity on a US passport to enter Hong Kong (that is, 90 day landing permission granted upon arrival, plus one month).

What I don't know is what if you have less than 4 months. If your "period of intended stay" is 5 days, then do you need 5 days plus one month passport validity to enter? One possibility is that if you have less than 4 months, you can't use e-channel for entry as an immigration officer must ask you to declare your intended length of stay in order to determine if your entry request is permitted.