试图 often implies the attempt was unsuccessful or is being described from a third-person perspective. It's more formal than 尝试 (chángshì, to try/attempt) or 想 (xiǎng, to want to).
usage
Compare: 试图 (attempt, often implies failure or difficulty), 尝试 (try, neutral), 企图 (qǐtú, plot/scheme — negative connotation).
