I read a novel when I was 14 or so who's premise is all about creatures inhabiting higher-dimensional space called "The Boy Who Reversed Himself" by William Sleator. I loved Sleator's books, they introduced me to really interesting concepts from theoretical physics as a youngun. If you find 4D Doom intriguing, I encourage you to borrow the book from your favorite ebook library, it's a quick fun read (at least, I remember it that way).

Fun fact: William Sleator's brother is the famous computer scientist Danny Sleator, inventor of the splay tree.

Part of Greg Egan novel Diaspora takes place in a universe with 5 spatial dimensions.