Based on your explanation, I would say that you need to write a personal narrative essay. Of course, there are more than five types of different essays. There are hundreds. If I have to list five types of essays, I would mention argumentative, persuasive, research, cause/effect, and compare/contrast. I would say that there are five types of expository essays, for example, though. I think you should not worry about the type of the essay but rather focus on the content of your writing. Your teacher will evaluate your essay based on how well you matched the requirements for academic writing.