Old thread, but I joined this forum just to respond. That's because I, too, am the owner of one of these nearly extinct unicorns. Mine's an RT5013 as well. 4-wheel steering, part time 4wd, part-time locking rear axle. 6 forward gears high and low, and 2 reverse gears high and low.
I also have a dozer blade/plow attachment for the front, a loader bucket for the front (the dump mechanism is manual/mechanical lever operated, not hydraulic, unfortunately), and a garden plough as well as a roto tiller for the rear PTO. I love the thing but it's definitely been a lot to learn when it comes time for any repairs because there is so little information and so few resources online. Honda stopped selling lawn tractors for the US market in the late 80's, I believe, so there are only a couple of youtube videos or other DIY guides or resources to consult with questions. Even with the factory service manual and the original owner's manuals for the tractor and the attachments, I still struggle to figure stuff out sometimes because I have no core knowledge or experience pertaining to tractors to start with (I know my way around a car, but that doesn't help me understand a front PTO clutch, for example).
Anyway, I've figured a few things out. I replaced the starter by buying one that wasn't supposed to be compatible and making it compatible. lol. If anyone on this forum knows their way around these things fairly well, please reach out and say hi. I'd love to know of someone I can pester with questions.