I am not an expert or even a adult, I am only 16 but I have ADHD and ADD and I experience all the problems you mentioned, except the social ones, and I'm sure that he will over come those as he ages. He sounds just like me, I don't know if that is how I was when I was his age but it certainly is how I am now. HE sounds like he has ADD rather than ADHD if he is shy and not bouncing around.
I find it very hard to concentrate, and am constantly reminded by my mother to get dressed in the morning, and I am in grade 10 now, however I am on the honor role and you say he is bright, I'm sure (with help) he will find strategies and work habits that work well for him and get the job done, and he will develop some problems but also solutions.
I would definitely not recommend holding him back because you think he has ADD, if it is an age thing I could understand, but I have lost interest in school, and you should try prevent that from happening to him. I find I focus extremely well when it is a project or activity I am interested in, for example my civics I'm around a 95% because I find law very interesting, and if he stays interested in school he may be able to stay focused at school in general.
A teacher's input is important, but not many teachers at the average public school have experience with ADD children, he will get in trouble sometimes, maybe even just because the teacher gets frustrated, but that is normal trust me. The teachers try to help and they do sometimes, but it is hard for them to understand that, I just don't have the abilities to sit still some days, but I am caught up with my work, and have good marks in my classes.
I have been in the situation musicmama suggested with the "office" at my school they were just like desks with little walls and a shelf, it was called a study carol. it does nothing, if he has social issues it will just make him feel like more of an outcast, and all the other kids just ask you why you are there anyway which is pretty distracting, and even after everyone stops talking to you, the walls just enable you to doodle and fiddle with pencils and things, and the teacher can't see you.
I would recommend trying grade one and if that doesn't go well then think about sending him back, but you have to give him a chance to try it, and it's not like he is missing anything by going to k late he has already done it all. but also if it is ADD a another year will not help him, he will not grow out of it, he just needs to adjust to it. and you should keep in mind all of the available medications, there are so many out there.
I know very little about ADD/ADHD, but I thought that problems with focus and attention were part of it. That being the case isn't it up to the teachers/Educational Psychologist to be coming up with some suggestions? It just maybe that at his age he will need repeated prompting/reminding and that is to be recognised as ADD and not 'being naughty'. For older children I have heard that it can be helpful for them to wear a watch that has a vibration timer. They can then set it to go off every 5 mins, and when that happens it brings them back to the task in hand. But he is only 5, so I think he will need extra adult support in class to bring him back to task.
It does seem like your child has some trouble holding his focus, but it doesn't sound too severe, or he would have these troubles at home too. You might try giving him an "office" to stand up at his desk to help him tune out other children. These are made by taping 2 folders together. Another trick is to place neon tape around the edges of his desk. It helps keep his attention on his desk so he can work.
As a teacher and a parent, I know you have an important decision to make. I have seen children go to 1st grade struggling. They were put back in K early in the year. All you can do is the best with the information you were given.
Good luck and God Bless