Wouldn't a 5-dimensional square be a hypertesseract? (10 'sides' each side is a tesseract.) This was a simple, fun shooter. I didn't think that the harder difficulty was actually harder than normal because you got the 5-way shot right from the start, while in normal you had the single shot for the first half, making things harder.
Bonus points in humor for title! Also, congrats, it looks like a fairly complete and nice entry. Could use some sound polish, but overall, it seems pretty good. I found normal to be quite difficult, but fair.
Simple game but well done. I included it in part 16 of my Ludum Dare 30 Compilation video series, if you’d like to check it out :) http://youtu.be/bMx3RCVCht0
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(very hard on a trackpad, though, but these kinds of games always are)