5 year diet
What they mean by diet history is that you have to prove you have had a BMI of 35 or greater with comorbidities or greater than 40 without for the last five years. In other words, if six months ago or a year ago you went from 200 to 300 pounds you most likely would not qualify. You just have to have your doctor(s) for the last five years show what your weight was during this time and it helps to also have them list your comorbidities during this time.
As far as a supervised diet, it will be either three, six, or twelve months with six being somewhat typical. This would be a diet supervised by your family doctor where you would generally go to a registered dietician or posibly your doctor could do it as well.
Who ever does it make sure they enter your weights into your medical record as you will need to show supporting records when you go for approval.
Jim Randall