My 7yo and 5yo sons have nasty fights. What is the best way to handle them?

Question

My 7yo and 5yo sons play well most of the time but continue to get into nasty fights over silly things and I see a lot of anger coming from both of them when the other does something annoying.
Here are two examples:
1) 7yo will start laughing at 5yo or keep singing a song that he doesn’t like, 5yo will ask him to stop repeatedly, crying, screaming and trying to hit him.
2) They were playing to give each other back massages, 7yo knows that 5yo does them a bit too hard but asked him to give him a back massage anyway, 7yo was squatting and when 5yo pressed his shoulders too hard he lost his balance, fell, got mad at 5yo and kicked him really hard.

My questions are:
1) Should I punish the one that hits by placing them in time-out or taking away a benefit like no tv later etc?
Usually I ask for them to tell me exactly what happened and tell them they should not hit each other and to apologize but I feel this is not enough and the fights keep happening.

2) I have tried to tell them to breathe or count so that they calm down but they say that doesn’t help them and they get even more mad. I asked if pressing a squishy ball would help, they said yes, is this a good idea?
What happens when they don’t have the squishy ball with them? 

Answer

1- No, punishment is not necessary for the person that hits. What is important is to name the reason why they hit. For example, you could say to them, “you were really disappointed that your brother forgot to do the massage softly and you hit them but next time I need you to walk away or tell them to stop and if your brother doesn’t stop, then walk away.”

It is the lesson on how to manage the conflict that is important.
All time-out and punishment teaches is how to avoid being punished so it’s not a good task at this moment because both of your boys at seven and at five are learning how to manage conflict. Punishing them because they get into conflict is like punishing a Toddler because they fell while trying to learn to walk.

2- All the techniques you named are definitely helpful, but remember the conflict between them is how they learn to manage every time they make a mistake. It’s naming a different way to handle the conflict and it is a “repeat and remind” situation.