Characterization refers to the ways that an author reveals the personality of his/her characters. This can be done by showing: what the character looks like; what the character says; what other characters say about him; what the character does (his actions), etc.
To analyze the character of Macbeth in Act V, Scene V, you need to look at the things he does and says, and how other characters react to his words and actions.
In Act V, Scene V, Macbeth is so confident of his strength and power that he mocks his enemy. His desire for power has become so strong that it squashes any other emotions in him. When he hears that his wife has died, he does not express much sadness or regret. It is not until he learns that Birnam Wood is moving toward the castle that he becomes agitated. At this point, his excessive pride leads him to his demise. He decides to leave the castle to fight and ends up dying on the battlefield.