Dunno about that particular tank, but lots of older "premium" tanks have a 3/8"-1/2" thick glass center brace ~8" wide silicone sealed in place under the plastic tank rim.. OTOH, if your tank really is 5/8" glass, it probably never had a brace...

It's one of the things I had to rework on my older Oceanic reef tank. The area to be glued wrt tank, frame, and glass piece must be absolutely clean and free of old sealant. I used superfine steel wool, acetone and paper towels as the final prep, taped the brace to a board across the top of the tank to hold it while the sealant set up. I used the original brace. A new one can be cut by a glass shop- just make sure it's exactly the same length as the side of the aquarium. Take the sharp corners off the brace piece w/ sandpaper before gluing.

Wait a week before filling so that the sealant will have full strength.