Why did Lady Macbeth want to kill the king?
Concerning Shakespeare's Macbeth, I can give you a couple of reasons why Lacy Macbeth wants King Duncan to be assassinated, but I don't know if I can find five.
First, she is ambitious just like her husband. She wants to be queen. This brings influence and power and wealth, or should, anyway. They're certainly wealthy already, but the crown brings new lands and castles, or at least one castle--Duncan's.
Second, she wants what men have, and what is denied women. She can't be king, since she's female, so her husband becoming king is the next best thing. Notice that we never even see Lady Macbeth out of the castle. She is trying to break free of the limited position her society allows her. She wants to get out of the kitchen, so to speak.
Third, she wants her husband to be king. I don't know that this is really a third reason or just part of the first two, but since you need to come up with five, I thought I'd list a third.
Ironically, once Macbeth is crowned king, he actually shuts Lady Macbeth out of the decision-making process. Once, he even basically tells her to leave the stage so he can be alone. She is reduced in her role of leading the nation, and even her own family. And she certainly doesn't get out of the kitchen.
dstuva has provided some excellent possible motives, but, the truth is, no one can know for sure what Lady Macbeth really wanted.
Someone asked a similar question here about Claudius in Hamlet. I think it is very telling that Shakespeare provides us with no motive for Claudius to kill his brother. One can come up with all kinds of theories about possible motives, but no motive is hinted at in the text of the play.
And the same goes for Macbeth. It is universally thought that the overriding motive for the murder of King Duncan was the ambition of Macbeth and Lady Macbeth. Fine, but what else is ambition than simply wanting more than you already. More power, more money, more fame, more...
It is this emptiness, this sense of one's dissatisfaction with the statis quo of one's life and the result of wanting more that drives people to do all kinds of things, even murder. It is Shakespeare's genius that he leaves motives out of the murders committed by some of his characters, for to his mind, the motive is never reasonable nor justified. Murder is pathological, an illness of the mind. Reasons are superfluous, meaningless and beside the point.