My Kenmore heavy duty 80 series gas dryer is currently at a state where it starts to work for five minutes then the heat quits. The dryer stays running and the clothes do not dry. What is wrong and how do I fix it?

You might have lint in the air box,( the part where the flexible 4" line connects) if you have a blockage in the air flow the burner will shut off on a high temperature limit switch.
Could also be in the flex hose or where it goes out side There is a screen there. Remove any lint that you can find, you may have to take the back off. Good luck.