The crossword solution for the term 'PLAYED CAT AND MOUSE (WITH)' is 'TOYED' (5 letters). This phrase is often used to describe a situation in which two people or groups are trying to outwit each other, with one side trying to gain an advantage over the other. It is derived from the game of cat and mouse, in which one player takes on the role of the cat and the other the mouse. The cat tries to catch the mouse, while the mouse tries to avoid being caught. In this context, 'TOYED' means to have engaged in this game of cat and mouse.