0. Don't pathologize. Even a correct diagnosis for ADHD doesn't mean something is broken.
1. Don't freak out. A person is not a diagnosis. The diagnosis isn't life threatening.
2. All sorts of marginally qualified people diagnose ADHD when children don't conform to some expectation...that's not to say that ADHD doesn't exist or that their aren't competent and compassionate experts. My gut, though is that these are more rare than pop-psychology or professional psychiatric ADHD diagnoses.
Here's the CDC page: http://www.cdc.gov/ncbddd/adhd/diagnosis.html
It requires at least six behaviors in each category plus all the mandatory behaviors. I would suggest that the interpretation of behaviors should be done by someone with a strong enough professional background in developmental psychology to determine what lies outside several standard deviations of normal behavior for a five year old child...i.e. the diagnosis should probably be biased toward false negatives rather than false positives.
The person making the diagnosis should be an independent health care professional, i.e. highly credentialed and not an employee or contractor to a school district.
3. Decide what behaviors might be problematic. Decide if any are actually serious enough to require immediate medical treatment. Those that aren't can be addressed gradually over time...children tend to grow out of behaviors all on their own. It's within the range of normal for five year olds to squirm, climb, and jump. Deal with problematic behaviors gently and compassionately in age appropriate ways.
4. A five year old should not be focused on school work unless it is interesting and fun. Neither should ten year olds. Our employers often pay us to work because it can be dull and unpleasant. We don't have ADHD.
5. Every child is different. Do you think the greater social isolation and focus on parent as the primary form of social engagement that comes with home schooling will benefit or deficit your child's long term well being?
Good luck.
https://en.wikipedia.org/wiki/Thom_Hartmann#Attention_defici...
Next I would probably seek to address any vitamin and mineral deficiencies, notably vitamin D, vitamin B and magnesium.
As for upbringing, I firmly believe you should seek to minimize anything that explicitly or implicitly can inflict guilt in your child. A good friend of mine has a wonderful son who is diagnosed with ADHD, and often the son would sit down and say to himself “Why can't I ever do anything right?” — and in his case I'd say that the guilt and self-loathing were a bigger problem [for the boy] than the ADHD.
I'm afraid that's all I can contribute with, but I wish you all the best.