Agree about you getting a professional opinion.
Years ago I cut a hole in my garage ceiling to allow operation of a small winch to help lift my hard top of my Jeep; however, the hole was smaller than the spacing between the ceiling joists (proper name for the boards you described).
The problem with doing a 5' x 5' area is that you will have to cut those ceiling joists, which is providing support to other elements. If you re-frame, add bracing, etc. it's possible to do what you want, but more details and specifics are needed. It sounds like you aren't familiar with any of this which is why I recommend you get a professional opinion.
Also, if I were going through these steps I would do a larger area than 5' x 5'. A minimum of 1 car bay, but preferably the whole garage. If you need to keep some of the ceiling level at 8' you could do a "boxed ceiling" to step up to the new height.
Something similar to this, but w/o the fancy trim since it's the garage...