Can someone please help me find a good example of Macbeth writing his letter to Lady Macbeth in Act 1, Scene 5?
There is no textual evidence or indication in Act 1, Scene 5 or at any place in the play that describes Macbeth in the process of writing the letter to his wife. If the play is performed and the director chooses to have a scene showing Macbeth writing the letter, it would be at the end of Act 1, Scene 4 because Macbeth tells Duncan he will contact his wife to prepare for Duncan's arrival:
The rest is labour which is not used for you.
I'll be myself the harbinger, and make joyful
The hearing of my wife with your approach;
So humbly take my leave. (I.iv.44-47)
Within the progression of the play, the time when Macbeth could have written the letter would have occurred between Act 1, Scene 4 and Act 1, Scene 5. There is no description of Macbeth writing the letter in the text of the play itself. Act 1, Scene 5 opens with Lady Macbeth reading the letter so, by this point, it has clearly already been written. We have to infer that Macbeth wrote the letter between Act 1, Scene 4 and Act 1, Scene 5.