Good question! There is one major conflict in Act Five, and that is the conflict between Cassius, Brutus and their army against Antony, Octavius and their army.
Another conflict exists between Antony and Octavius. Immediately before they speak with Brutus and Cassius, Antony and Octavius are arguing about battle plans. It seems as though Octavius is inheriting some of his uncle's arrogance, because he seems unwilling to listen to Antony's advice, though Antony is a more experienced soldier.
Cassius and Brutus both seem to be having an internal conflict about whether this battle is the right thing for them to be doing. Cassius confides in Messala that today is his birthday, and it feels appropriate that he'll die on the day he was born. He also explains that he saw scavenger birds (vultures, etc) replace the eagles that once flew over head. Though at the beginning of the play, Cassius didn't think any omens pertained to him or his plans, he is now certain that he will die.
Brutus doesn't come out and explain his fears as much as Cassius. Cassius wants to know what Brutus will do if he is captured. Brutus explains that he will not be taken to Rome as a slave, but will not commit suicide, as it is cowardly. Brutus' conflict regarding this issues is sure to come to pass, as he and Cassius say goodbye, as though they are never to meet again.