This is large project. I would recommend consulting a professional or finding engineered plans for aquarium construction online.
An aquarium of this size will require its own dedicated frame. The empty tank will weigh about 275 lbs. Filled with gravel and water, it will weigh about 1500 lbs or 0.75 tons. Inspect the floor and joists in the area you plan to place this aquarium for structural integrity.
If you construct it 60x24x24 (LxWxH) you'll have to build a custom frame. I recommend building a more standard dimension for a 150 gallon: 72.5 x 18.5 x 28.5 (LxWxH) inches and purchasing a standard frame.
You'll notice that 72.5 x 18.5 x 28.5 equates to more than 150 gallons. That is because this size is designed to hold 150 gallons of water and 15 gallons of gravel, decorations, etc.
From my experience, 150 gallon aquariums (72.5x18.5x28.5) use 5/8" thickness glass. This thickness might be appropriate for your build, but do not take that as direction to proceed. The thickness of glass should be chosen by someone who knows how to design it.
You should consider the type of glass for your aquarium as well. Tempered/laminated for example is much safer if the aquarium fails, but will not allow bulkhead fittings to be drilled through glass.
Further, you must use a silicone with a designed tensile strength. Awhile appropriate as a an ornament adhesive or sealant inside an aquarium, GE Silicone I is not appropriate for aquarium construction.
