Act I scene 5 of Macbeth begins with Lady Macbeth reading her husband's letter. This is the first soliloquy (lines 1-27) is she is alone on stage. After she reads his letter about running into the witches, she thinks to herself that he may not be man enough to carry out the needed task. She asks to lose her weak, womanly ways in order to be strong enough to motivate Macbeth.
Later in the same scene, Lady Macbeth is again left on stage (line 39). The messenger informs her that her husband is on his way with King Duncan. She again plans out the steps he will need to become king; she plans for her husband to kill the king in their house.
Scene 7 begins with Macbeth's soliloquy. In these lines (1-29) he worries about the task he must undertake. He questions killing Duncan since it is not just a sin to kill, but to kill his king while he is a guest in his house is unforgivable.
The word "soliloquy" is derived from the Latin adjective solus, which means "alone" and the verb loquor, which means "to speak." Thus, when searching for a soliloquy, we want to look for a single character on stage and delivering a speech.
In Act 1, Scenes 5 and 7, we find three examples of this. The first two occur in Scene 5. This scene opens with Lady Macbeth reading reading a letter from Macbeth. Even though she is technically alone, the letter is a sort of meta-character present with her. Thus, this is not, technically speaking, the beginning of the soliloquy. The soliloquy proper begins after she finishes reading the letter and says "Glamis thou art, and Cawdor; and shalt be". Soliloquy's are usually thought of as revealing a character's inner thoughts or feelings and the reading of Macbeth's letter does not fall into that category.
Later, in that same scene, Lady Macbeth has another soliloquy that occurs after the exit of the Messenger and before the arrival of Macbeth. This soliloquy begins, "The raven himself is hoarse". In this soliloquy, she begins to steel herself with a view toward the murder of Duncan.
The third soliloquy in these scenes begins Act 1, Scene 7. Here, Macbeth himself open the scene by saying, "If it were done when 'tis done, then 'twere well". In this speech, he muses upon the murder of Duncan that he is about to undertake.