A couple of quick thoughts.
1) Will your district accept the private testing to get him into the HG program? Our does...
2) It sounds like he would be in the right place in the HG program. Don't worry about the grades too much. One of the benefits of the program is that he'll be exposed to smart peers and higher level thinking.
3) If he has anxiety / inattention that is diagnosed, can you get him on a 504 or IEP? That way he can get accommodations that will help his academic performance.
4) He's only in 5th grade and has a long way to go. Try to relax, kids change a lot. We saw a huge improvement in our son who is soon to be 15 during 8th grade. He's HG and not 2e, but he really got his act together and now is very self-motivated and studies hard.
