While I'm not a computer programmer, I am a full time composer/arranger of music. In the music world, it would be breaking copyright law and quite illegal for me to arrange someone else's song and publish it for free. Even if it was because I just love the song and wanted to get it out there for people to enjoy, and I didn't profit from it at all, it would still be illegal and breaking copyright law, without having express written permission from the publisher.
Now that doesn't mean it doesn't happen, there are certainly people that do that, but it's illegal, and every now and then the publisher will find them and file a big 'ol lawsuit. So, similar to what you've found in the app store, I'm sure there are some 5/3/1 apps out there, and I guarantee none of them got Jim's permission. The process of filling a lawsuit can be long, drawn out and quite expensive, which may be why Jim hasn't done so, or he may not know they're there. Still, even though you're not trying to be malicious, you should have his written permission before proceeding. If you're only using it for yourself, I don't think that would be a problem.