How does Brutus change his opinion about the need for Caesar's death in Act 5 of Julius Caesar?
You must remember that the decision that Brutus makes to join the conspiracy is because he fears what will happen to the Roman Republic should Caesar be crowned and given total power. He is a good friend of Caesar's and thus the betrayal is compounded.
Is Brutus correct in his fears for Rome? Yes, he is. If he had tried, was there perhaps a better way for him to fight for the future of Rome than killing Caesar? Perhaps.
Does he feel guilty? Of course he does. At the end of Act IV he is visited by Caesar's ghost. When he and Antony exchange words in V. 1, Antony lays a guilt trip on Brutus. His final words as he runs on his sword are telling, "...Caesar now be still./I killed not thee with half so good a will."
He did not kill Caesar out of spite or envy. Antony is right to call him "the noblest Roman of them all".
He had sincerely believed that once Caesar was no longer a threat, Rome would continue with government as usual. He did not foresee the civil war that ripped the Republic apart. The Triumvirate was successful and Octavius became Augustus Caesar, the first emperor in the Rome Empire.