正解 is used commonly meaning of "correct answer". 正しい means just correct or right. ex:(正解) when you have a question in school, you can ask your teacher "is this a correct answer?" ex:(正しい) when you lost on the street, you can ask someone "is this the right way to get to ～?" bothe of them are very similar, but 正解 is a noun, and 正しい is an adjective.