You can’t make the circuit with your specification.
For your requirement you need to drive 19VA (17.2VA in secondary) in the primary side with 6V. So the switching current will be 3.2A. It will exceed the current limit of the controller.
As per data sheet it will work.
Select transformer with primary inductance of 30 to 40uH and ratio of 1:1:0.5,
Put a heat sink for IC,
5V out should not be a regulated one.