The GBR goes as far south as Bundaberg, which is about 350k's North of Brisbane and tbh is not the the best place for seeing the reef. If you want to see it in all its glory I would say you need to be North of Mackay, which means you really are better off going to Cairns if for no other reason than it is set up to handle reef tourism better than anywhere along the coast.

With 4 or 5 days you could probably start in Cairns and make your way down to Mackay, that way you can see Airlie Beach, Hinchinbrook Island as well as the reef.