What is the weight rating of your trailer?
You might want to check out plans from e.g. Glen-L. Even if you don't follow one of the exact models, the construction methods and systems are similar. For a trailer, building something that is fairly lightweight but still sturdy enough is a big part of the job. In that sense, it's rather different than building a shed, where weight really isn't much of a concern.
A 5x10 travel trailer is going to be rather smaller than you imagine. Even if you extend the width somewhat beyond the utility trailer deck (since you don't really need wheels outside the edges of the trailer) it's still quite small. You'll have a pretty hard time making something usable by a family without some significant compromises, like not eliminating the bathroom or the kitchen or requiring some people to sleep in tents.
If you want the challenge of the project and need something to do, by all means go for it for that reason. But if you're interested mainly in something that makes financial sense, I think you'd be much better served to sell your car and your trailer and buy a used travel trailer. Even if you're building your own, it might make sense to buy one just for the appliances and fixtures.
The idea of a making a school bus conversion (or perhaps a step van conversion) does have a good bit of merit. You'd end up with a much more useful RV in the end than you would based on your trailer.
Anyhow, that's my opinion.