Wow. I can totally relate to your description of your days. I was recently diagnosed (am almost 40) and suddenly my whole life made sense. But, I had been clinically depressed for almost 25 years and nothing really "fixed" that. I am telling you, I spent a lot of time in meditation, ate healthy foods (even went vegan for a while), took every antidepressant you can find, and the older I got, the more I really needed to know the answer because it was affecting every aspect of my life, especially my work.
I started Adderall about a year ago and the difference is astounding. Dr.s use Adderall as a diagnostic. If you respond well (and they check your pulse and heart rate in addition to your feedback), then chances are that you have ADD and can be treated. That was the case for me. I got a second opinion, too. I didn't want to be "swayed" by any drug-related euphoria, so I took myself off and went to another Dr. - same diagnosis. I even had to take my school records, get family feedback, etc.
I never felt like I could do grad school because of this, but now I know I can. As a kid, I had psychiatrists wondering why I had so many problems focusing in school when my "scores" were so high, but all they told my folks was that I was bored and needed a challenge. I ended up majoring in Math, loved it, found it challenging, but still had a horrible time focusing - just exactly like you mentioned with the 5 minute or 30 second days.
I am in the process of a move right now and am in between jobs, so I cut way back on the meds. But I know that when we've relocated and I am working again, they will make a huge difference. I intend to finish that master's I started 6 years ago and know that I have something that finally works for me. Please go to the Dr. No matter what anyone says, it can close a lot of gaps and answer so many questions in your life. Good luck!
PS - I am an educator and am very comfortable working with kids with ADD. Many teachers aren't but many are. The importance of that skill is determined by the Principal (and many of those were poor teachers to begin with). So it is a dice toss about what kind of teacher your kids get. All I can say is that I wish someone had encouraged my folks to consider meds when I was in school. While I ended up getting my Math degree, I was in therapy every week so as not to "sabotage myself". I truly believe medication would have made a huge difference in the development of my confidence, success in school and self-esteem in general. Some kids have to take meds. I always knew I was intelligent and could never understand why I couldn't translate that into my life on a regular basis.