I have a tuck under single car garage in my bungalow that currently has carriage doors that have seen better days.

I would like to replace the carriage doors with an automatic (and insulated) door, however, everything I've seen seems to require a minimum of 7" of clearance between the top of the door opening and the ceiling of the garage. My garage only has 5" of clearance.

Does anyone have experience with garage door solutions that will work for this small amount of available clearance?