It sounds like your son's preschool teacher is seeing things that you are not seeing and vice versa. That's very, very possible and normal. Still, ask for a meeting with her so that you can sit down and really listen to her concerns. There probably are some skills that your son doesn't have that would be helpful for him to have in kindergarten (or young 5's). No shame in learning what they are and consider helping him with those.
Remember, just because he's not 100% clicking with preschool doesn't mean he will feel the same way in August. He is going to grow and change a ton between now and then. Also, young 5's is a different program with a different school and a different teacher. He might click better than, so try not to get too far ahead of yourself.
My oldest did a year like young 5's and started kindergarten when he was 6. Best thing for him!!! He's in 5th grade right now, and I am so glad he's not in 6th. He belongs in that age group. He's doing great, and he is where he should be.
Now, it's great that you did the school's special ed evaluations. Hopefully you learn somethings about your son, both things that he's good at and things he can work on. It's always helpful to learn those types of things. But do keep in mind that a school's special ed evaluation is not in any way equivalent to a psychologist's evaluation. If you son really does have any type of diagnosis, it needs to be done be a psychologist. I'm not saying he does (believe me, I am not even remotely qualified to do that, even if I did meet your son).
Based on the concerns you mentioned in your previous post, he needs to be seen by a psychologist, and a school evaluation isn't going to be enough. School evaluations are very narrow. They are only looking at whether or not he has very specific needs in specific academic areas. The concerns you mention actually fall more in line with Occupational Therapy, and that is not something a school is going to be able to address.
If the concerns you had in your previous post are still valid, you need to schedule an appointment with a child psychologist and have him evaluated.