Sounds like my SD to a T when she was in first grade! The teacher started making sounds like "She has ADHD" but she really didn't.
For one, she was on the young side. You might not think that a few months make a big difference, but they really do! Her attention span just wasn't there yet.
My SD is a dawdler. I know she doesn't have ADHD because she can focus on things she's interested in. The problem was, she just wasn't interested in school. She was a social child, so it was much more interesting to goof off instead.
My SD needed lots of reminders to do her tasks. She would get off track easily. She also is the S-L-O-W-E-S-T eater I've ever met!
Here's what worked:
1. I would set a timer for chores. If she finished the chore before the timer went off, she'd get a reward. I would give her plenty of time. If she didn't finish in time, I usually would tell her "okay, well I will give a few more minutes to earn your reward." Then I'd stand there to keep her focused. If you don't do this, then she will get upset and not want to finish the task. The goal is to help her keep focused. Never give her a task that takes longer than 5 minutes. If you must, break up the task into 5 minute segments.
2. I remove distractions. This ESPECIALLY includes the TV!
3. For school, I give her a certain amount of time to do her work. If she finishes, she earns playtime. If she finishes early, she can have the extra playtime. I break up schoolwork into chunks. I use a timer. This has always worked, and she usually focuses on her work, gets it done and enjoys her playtime!
Sometimes she needs me to stand there and push her through. For example, she used to take 30 minute showers! So I had to set timers for a shower. If I needed her to just get it done, I had to stand there and direct her. It's just what you have to do.
I always use free time as an incentive. For eating slow, my husband and I will bring out the dessert and then say "if you're not done eating, you won't have time for dessert!"
My SD worked well with checklists. Sometimes she'd get overwhelmed with what she thought was a lot of work so she'd just give up and goof off. She had checklists for everything and it worked! I put the lists in plastic sheets and she'd use a dry erase marker.
My SD is 11 now. She focuses on her chores without the timer. She takes reasonable showers. She gets ready on time. She eats at a normal pace. She gets her school work done without too much hassle.
You just have to keep working on it at home. It'll happen for you! Be patient. Every child has a different personality. It doesn't mean they have ADHD. Personality defects aren't diseases! Not everyone is perfect!
Also, once my SD got a better concept of time, that helped her to not move so slow. Some young kids have no conception of time or time passing. Once they get that awareness, that helps too.