There are a few details that are missing from your question, so I am going to have to make a few assumptions. I do not think that you mean a world history textbook. So I am going to recommend historical fiction that focuses on world history. The other assumption I am going to make is that you don't need the book to cover 5000 years of history, just a world history time, place, and event.
First recommendation: "Masada: The Last Fortress" by Miklowitz, Gloria D. It's about the Roman army and the war against the Jewish zealots that hold the mountain fortress of Masada.
Second: "The Midwife's Apprentice" by Karen Cushman. It's a children's novel, so I'm not entirely sure how your professor is going to react to that. But it is short and a quick read. It is set during medieval times.
Third: "Mary, Bloody Mary" by Carolyn Meyer. It's young adult literature, and around 220 pages. It tells the story of Mary Tudor and King Henry VIII. Carolyn Meyer has a few books set during this time period, and her historical fiction is usually quite fun to read.
Fourth: "Memoirs of a Geisha." It's a prize winning book focusing on Eastern culture.
Fifth: "The Pillars of the Earth" by Ken Follett. It's good, but not short.
Sixth: "The Boy in the Striped Pajamas." Takes place during World War II and is about two young boys. One a German and the other a Jewish prisoner.
7th: "Kydd" by Julian Stockwin. The entire series focuses on the British Navy during the Napoleonic Wars.