Typically, the frame holds the material to be displayed, artwork a photo, etc. In this case, I would lean towards having the back, mounted inside the frame of course, support the weight of the map and the frame.
Didn't know you could get Plexi in a 60" X 120 " size. It would not be my first choice in protective materials, it's soft and scratches easily, and without extreme care, will crack easily. Glass would weigh too much for a removable/changeable display case. Since it's changed out so often, could a protective coating be applied, without an additional cover? Are these maps kept and stored or disposed of after display? If stored, how? flat or rolled up?
Because of the extreme dimensions, 5 ft X 10 ft, which exceed nominal plywood sizes, 4ft X 8 ft, you may have some procurement issues. In addition, getting this thing on and off the wall will require 2 people, minimum and the ability to lay it out flat and change out the maps.....
This is a challenge I personally would not take on. The restriction on materials is definitely a limitation I would not want to deal with.
One solution is to project the image on the wall and be done with it! Change the image every 10 minutes if you want.