The thing that is probably causing the breaker to trip is that something is heating up during the five minutes of run time, and then the load is increasing. I would recommend the following course of action. Run the dryer to failure. Physically check by touch the dryer outlet and dryer cords. If they are unusually warm to the touch, you have a loading problem. If the cord is cool, but receptacle warm, the receptacle probably needs checking. If the cord is warm, the dryer is getting too hot.
With regard to the lint trap. ... a little confused about your message on this, but if the lint trap is glued shut, your dryer is overheating and throwing the breaker as it loads.
It sounds to me like the dryer is getting too hot, increasing the load in the circuit, and tripping the breaker. I disagree that the problem is in your breaker panel. At any rate, be very careful with anything you do at the breaker panel. Remember the bars in the back of the panel are live if the main is on, and unless you have a service disconnect, there is a lot of juice there!