no advice here (thought you've gotten some good stuff), I just wanted to comment that anyone who can carry an egg, wait for a rear, and then have the calm presence of mind to break it over their head at the height of a rear is my personal hero. =p
Yes, most absolutely you do! It is not only your safety at risk here, but any and all future riders/owners of this horse. I agree with Kayty on warming up first, my TB is cold backed and really needs to be warmed before riding- it is night and day with him. I may have missed it, but also most importantly, make sure he doesn't have any soundness issues causing these outbursts. I doubt a 5 yo TB is having growing pains, they mature more quickly than many breeds and he should be about done by 5.
I'm not sure if you have the right match in your trainer. Why isn't the trainer stepping in to help you with these problems instead of having you try to lunge him to warm him up for her? If you are having problems giving him the right idea on the ground your trainer should be helping you to get things going in the right direction.