I thought so , too.
If we check in 5am, we have to check out by 5am, but if we check in after 9AM, we have the late check out platinum benefit as 4pm check out.

I guess 5am is very very early check in.
I do not think the hotel assume that early when they say early check in is allowed if the room is available.

I had several experiences some hotel allowed me to check in after 7am, and I really appreciated their kind offer.

If they said NO, I will pay or store the luggage and stay at the lobby lounge until the front desk people say Please Check In(5am is not a good time to walk around the Ebisu although it is perfectly safe).