My son is also 5 3/4 almost 6. He starting writing books a few months ago. Surprisingly the spelling is pretty good, IMO. I usually tell him just to do his best and I will help him spell it correctly after he at least tries. He also gets creative and usually uses books that he owns to find the word he wants and then copy the correct spelling.
So far he has written a book on the Solar System and 4 short stories on Halloween Characters. He calls them his fall series. He actually started writing a chapter book this past weekend that is starting to resemble the movie Monster House. His goal is to have at least 8 chapters with some illustrations.