Does an oral agreement and a handshake hold up in court?

The situation: Father Harry dies and leaves farm to his 5 sons. Deed states that if one of the 5 should die, his share goes to his family. Son Mike asked the other 4 brothers if he could have an acre or so of road frontage in order to put in a doublewide house. The other brothers said they would let him have this land if Mike understood that this parcel would be his total share of the farm. Mike agreed to this and they all shook hands. The parcel was divided off from the farm and put into Mike's name and he put in 2 houses. Then Mike died and his son and wife are saying they still own 1/5 of the farm because of that original deed. What can the remaining 4 brothers do now? They failed to put the agreement into writing but all four of them were there when they shook hands on it.