In High School, I was "taught" to write five-paragraph essays (and when I say "taught," I mean "forced.") The five-paragraph essay was the only form allowed in Sophomore English class. Any deviation from the five-paragraph essay form was punished with a low grade. For example, the parenthetical aside in the first sentence of this paragraph is not specifically on-topic and would have resulted in a half-grade reduction on the essay. As a result of the instruction I received in writing essays, I concluded it is a very stupid way to teach young people to structure their thoughts.
Each paragraph of a five-paragraph essay must contain at least five sentences. The sentences may be as long or as short as you want to make them, but they must all relate to the same common theme. Even if you have nothing more to say about a particular idea, you may not end a paragraph until you have written five sentences. If you end your paragraph before you have composed five sentences, you will receive a negative red comment and a lower grade. I know; I tried.
Shapes are very important in the five-paragraph essay; specifically, funnels, hourglasses, and pyramids. You see, the essay itself must have a shape, and each paragraph within the essay must also have a shape. Funnels take a broad idea and then get progressively specific. Pyramids, on the other hand, start with a specific and then get broad. Based on those two descriptions, you can probably figure out what an hourglass essay does; I always thought there should also be a Santa-shape.
Every paragraph in a five-paragraph essay must have a topic sentence, because a reader will never know what you are writing about if you do not come right out and state it explicitly. In the case of this paragraph, the topic of the topic sentence is the topic sentence itself--how meta is that? (I just lost points for going off-topic, and also for using a dash, which my English teacher hated for some reason and would have circled in red; I also just lost more points with this parenthetical aside, but it's a sentence, an therefore it counts toward this paragraph's sentence quota). All sentences following the topic sentence should relate directly to the topic sentence, or you are not writing right. This paragraph, about topic sentences, does not have a shape because it went off-topic, and with all the other deductions piling up, my grade on this essay will therefore be no higher than a C.
Finally, of course, a five-paragraph essay must contain five paragraphs. Even if you think you are finished writing about your essay topic (which does not get its own topic sentence), you cannot simply stop writing. What you must do in that case is summarize your main idea for the reader. If you follow the reliable old tell-em-what-you're-gonna-tell-em, tell-em, tell-em-what-you-told-em structure, you really only have to write three original paragraphs between your introduction and your conclusion. In conclusion, the five-paragraph essay form is a really awful exercise in rigid form for its own sake which sucks all the joy and creativity out of the act of writing, and which should be relegated to the compost pile of instructional history forthwith.