Yes, CM can work studying Black History. Look for books written by one author with a passion for his/her subject. You want books that make the subject come alive without talking down to the child. Consider autobiographies, books written in a conversational tone, and books written in narrative (story) style.
We just finished reading a nice biography of George Washington Carver by David Collins. I believe that series (called the Sower Series) also has a biography on one of my favorite singers, Mahalia Jackson. Amos Fortune, Free Man is another one of our favorites. I think all three are recommended for grades 4 and up, but I’m sure you’ll find good living books that are appropriate for your 5 year old too.
Please do use your own books; the key is to make sure they are living books. Don’t feel you have to limit yourself to just what is presented on this site. The books recommended here are only suggestions. I think almost all CM moms are constantly on the lookout for more living books everywhere they go. 🙂