Peak and Peak may not be the same thing.
From page 1 the peak gate current is 5A. That is the drop dead current.
From page 2 the gate trigger current is typically 3mA but it could be as high as 32mA and it could take as little as ?mA to trigger the gate.
In other words a 3mA gate current will trigger 50% of the parts. A gate current of 32mA will trigger 100% of the parts. In production I would hit it with 60mA.
There will be some parts that are happy with 1mA