When someone is described as "sphinx-like", it usually means they are mysterious, inscrutable or enigmatic, much like the famous half-human, half-lion statue in Egypt. However, there are other ways to describe this type of person or situation without using the same old phrase. For instance, you might say they are reticent, uncommunicative or have a poker face. Alternatively, you could use words such as secretive, cryptic or enigmatical. Essentially, any word that suggests an air of mystery or a lack of clarity can serve as a synonym for sphinx-like. It's all about finding the right phrase for the context.