Romeo, in Mantua, contemplates a happy dream he's had: Juliet found him dead, and brought him back to life by kissing him. As Romeo muses on love, Balthasar, Romeo's servant, arrives with news: Juliet is dead. Balthasar saw her laid to rest in the Capulet tomb.
Romeo's dream is the opposite of what happens. Rather than bring him back to life, in act 5, scene 3 Juliet kisses his lips to try to join him in death.
Romeo shouts, "Then I defy you, stars" (5.1.24). He orders Balthasar to get him paper and ink for a note, and to hire some horses. Balthasar asks Romeo to calm down and be patient—he says that Romeo's "pale and wild" looks signify that Romeo is about to do something rash. Romeo assures Balthasar that he won't do anything crazy. Balthasar exits to get the paper and the horses.
Romeo seeks to deny fate by joining Juliet in death, but is actually playing into fate's hands. Part of the genius of Romeo and Juliet is how its characters' personalities determine their fates. Also, note how Romeo, like Juliet did before, has now started to lie to protect his privacy.
Romeo addresses Juliet, telling her "I will lie with thee tonight" (5.1.34). He finds a poor apothecary, and asks the man to sell him poison. The apothecary says Mantua has a death penalty against anyone who sells poison. Romeo says the apothecary should not pay any attention to the law, since there is no law that protects the apothecary from his poverty. The apothecary sells Romeo poison, saying "My poverty but not my will consents" (5.1.75). Romeo takes the poison and heads off to Verona and the Capulet tomb.
Romeo tells the apothecary to break the law because the law doesn't do anything to help the apothecary out of his poverty. But Romeo is also unwittingly describing his own situation: the law cares nothing about his love, and so he's breaking it. By buying poison, Romeo throws off the last of the social bonds constricting him.