I would start with the interocular trauma test: plot the data, look at it, and see if there is any pattern that "hits you between the eyes". I would start with five histograms of the five test scores and compare those. (actually I would not, I would probably compare quartile plots, but it takes some training to read those.) If you want to use the results to tailor your courses to your students, then I guess that is enough.
What a formal statistical test can give you on top of looking graphs, is that it can protect you from seeing a pattern when you actually have random noice.