There is so much that I want to say to this - especially because I see so much of myself in your posts.
To start with, it is extremely unfair and inconsistent to threaten to put him in rec classes because you don't like his focus in the gym. First of all, he obviously knows that his gymnastics is important to you. Threatening to pull him out of classes that you obviously want him in is telling him that you don't think he's good enough. I would guess that some of his reaction to rec classes is because he KNOWS it would mean disappointing you. Please PLEASE give this kid a break.
Secondly, continuing to threaten consequences without following through undermines everything in your relationship with him. If you say "Don't jump in the pit during class or you're going back to rec" and then WATCH him jump in the pit during class without sending him back to rec, you are showing him that your words don't matter and he's going to stop listening to you. Kids crave consistent, fair boundaries. Part of their job is to test those boundaries, and part of our job is to make sure we enforce them the same way every time. We cannot use consequences that we are unwilling to follow through on. Every time you've threatened rec classes for his behavior and not followed through you've undermined those boundaries a little more while at the same time increasing your stress and obviously increasing his stress. Your 5 year old should not be "balling" and begging to go to the gym because of conversations with you, it is unfair to him, unfair to his coaches, and unfair to yourself. You can't be enjoying these interactions any more than he is!
Finally, most children respond much better to positive feedback than to negative. Instead of focusing on the parts of practice you didn't like, try to focus on what you did. So, you could say, "I really liked how you went straight to the mats when your coach asked you to - way to go!" Or, "I saw you listen well to your coaches 3 times today, do you think you could try to listen that well 6 times tomorrow?" Or, "I love that you remembered not to jump in the pit in the beginning of the class - next time let's try to remember not to jump in the pit at all okay?!" Or, better yet, STOP watching this poor kid's practice for a while. Let his coach deal with behavior issues in the gym, you'd be amazed at how healthy it can be to just back off and let your son handle his sport with his coaches. You said yourself in another post that you feel he's mature enough to get himself ready to go to the gym - then why don't you feel like he's mature enough to handle his own practices? If the coach needs your help with his behavior, he or she will ask for it. Mostly likely, his coaches recognize that he's a little boy with lots of energy. More than that, if you're watching every practice and commenting on his behavior for them they probably don't want to pile it on. Give your son a chance to succeed and his coaches a chance to prove that they can teach your child.
I know this is coming off as harsh, but I feel like you continue to ask the same basic questions and you continue to get the same answers from us. Every child is different, we aren't there with you, and you know and love your child. BUT there are lots of parents of lots of talented kids on this forum (which you came to for advice) and in almost every post these parents, coaches, judges, and athletes are advising you to back off and let your child enjoy his gymnastics. I hope that you can hear this advice and know that it's coming from a place of love and concern.