In Act 5, Scene 1 of Macbeth, does Lady Macbeth repent of her crime, or is she merely suffering from remorse?
Remorse is feeling sorry for what you did. It may be that you regret what you did or not. It does not include a need to confess but does indicate a pang of conscience.
Repentance includes regret for what you did and a desire to reverse the situation if it were possible. There is also a need to make things right and a determination not to repeat the crime. With repentance, you must confess your sin in order to move forward and make amends for what you did.
Both include intense feelings of guilt.
Lady Macbeth is indeed haunted by her actions and definitely remorseful. In this sleepwalking scene, she does basically confess her sin - "Who would have thought the old man to have had so much blood in him?" - but her rantings only serve to confuse the doctor and attendant.
The doctor knows that
Do breed unnatural troubles; infected minds
To their deaf pillows will discharge their secrets
but he cannot understand or contemplate the extent of her collaboration. It is too terrible to "think, but dare not speak."
It is certainly true that it is her recognition of the extent of what she and Macbeth have done that drives her to suicide
the stain of sin having eaten away at her mind
but as she is no longer aware of her surroundings, she, despite confessing, cannot be said to have repented. She seems more to need to confess in an attempt to clear her conscience (which clearly fails) rather than out of any real regret.
Lady Macbeth does, even in her time of madness, still feel protective towards Macbeth, attempting to comfort him (even though he is not there )
Wash your hands, put on your nightgown...Banquo's buried
and does make the reader or audience feel some compassion towards her but again is not indicative of repentance. It is perhaps her only nurturing and womanly feature but she has concern for her husband ,not sorrow for what happened. She worries that he will be caught but her torment is not caused by a wish that they had never conspired but that it causes so much guilt to surface - something she did not anticipate, having supposedly mentally prepared herself well in advance. She would even feel nothing at killing
a baby at her breast to honor a vow.
She consistently steels Macbeth to proceed with his ambitious plan to be king - with or without the witches help. Knowing that as long as the are careful "a little water clears us of this deed."Nobody will even know what they have done. Perhaps losing Macbeth's trust is part of the reason for her descent into madness as she is no longer needed by him. Definitely not a repentant woman!
My feeling about the play is that Shakespeare wanted to make Macbeth look like a basically good man who committed a bad deed partially against his will. Lady Macbeth played a prominent part in the original crime of murdering King Duncan, but then she drops out of sight during the middle of the play, after having serving her principal function of goading her husband into committing his terrible deed. I suspect that Shakespeare felt he couldn’t just forget about Lady Macbeth, since she had been such a dynamic figure, so he wrote in a scene at the end in which he finished her off. Macbeth was strongly attached to her and dependent upon her in the beginning, but at the end he doesn’t seem to care in the least that she is dead.
She should have died hereafter.
There would have been a time for such a word.
He has probably grown to hate her because he knows he wouldn’t have killed Duncan if it hadn’t been for her relentless pressuring. How Lady Macbeth feels at the end does not seem important to me. I sense that Shakespeare just wanted to display her to his audience and then dispose of her (which he does offstage). She may feel haunted by guilt and fear of divine punishment. She may feel remorse that by driving her husband to commit the murder she has gained the regal status she wanted but has irrevocably lost her husband’s love and even incurred his hatred. It is significant that they do not appear together at the end but are isolated in separate rooms. Shakespeare did not want Macbeth to be regarded as a pure villain, like Richard III or Iago for example. He imposed a lot of the guilt on Lady Macbeth and evidently wanted to show her being punished at the end of the play. She probably realizes that it is not only her husband who hates her, but everybody in the kingdom. She is wretched and alone.