[Anne]

If you do nothing then nothing will change. The only difference will be that your dog will get more aggressive as he gets older. He is exhibiting this behaviour because he hasn't been taught that it's unacceptable. At the moment the puppy is calling the shots.

If I were the owner of the 5 month old bulldog puppy I would be furious that you had no control over your pup and allowed it to attack my puppy. Most of us do our best to protect our puppies from bad experiences. I hope the bulldog doesn't think it now needs to protect itself from all other dogs.

You need to take this dog to obedience training so that you learn how to train him and he learns to respect and trust your leadership. If I were you I would seek out a good private trainer who is very experienced with the breed.

What do you do while all this action is happening between your puppy and other dogs?

Until you have the situation under control please don't take this pup off leash anywhere it's far too dangerous not only for your dog but for any other dog he may come across.
If things are allowed to continue as they presently are there is a good chance you will lose your dog. Either it will be killed by another dog or animal control will seize the dog for being a dangerous dog.

I wish you the best with your puppy. You need to take some action now, before the behaviour becomes totally out of control.