ADHD is a bonafide brain disorder that affects the brain, just as diabetes affects the body. I've two kids and a husband with it, I'm a teacher, and I worked at a school for students with learning disabilities. He can overcome this, but must be taught. Repeatedly. For years. You will need to enlist the help of his teachers to ensure he turns the work in. If they won't, request an IAT meeting.
You may have to try several things for a few weeks at a time to see what works. I would suggest first trying a homework folder.
Another suggestion is to color code ONE binder for him and purchase tab folders with pockets on both sides (front for homework, back for papers to keep for the unit). Each week, go through the binder with him to remove old papers. Don't throw them out in the event they are still needed for the unit! Keep in another folder by subject at home.
At school, work with the teacher(s) to ensure his homework IS turned in. You may encounter some that may cooperate briefly then expect him to be responsible. This is when you need to intervene. Nicely. Most children with learning disabilities average 2-4 years behind in maturity, therefore, a 5th grader may be operating like a 1st-4th grader in responsibility. LD online is a good resource. Find out if homework checks are occurring, see if a study buddy or student homework partner (that will check that he turned it in) might benefit him. Create, or ask the teacher to create, a homework checklist that is kept on his desk each day. One teacher at my son's school makes all the kids get up at the same time to turn their homework in (this is 7th grade) and as each child hands it to her, she checks off their name, or, hands them a slip that it wasn't turned in. This teacher has been VERY effective with my son in his least favorite subject largely due to this very simple method.
Best of luck to you, and feel free to pm me if you have questions anytime.