The five minute a rule per month is one of those rules that really has no evidence. A bit like 5 a day of vegetable.
However exercise that’s not appropriate for a puppy’s age and development can cause significant and irreversible damage.
I would not be ball throwing for any dog ever but definitely not a puppy. You can play ball eg catching it or sniffing it out, maybe running to a still ball.
I would be encouraging interaction with other dogs and children but again I would restrict it. Partly to stop the puppy from getting over stimulated but also to stop it damaging joints etc.
You will find that training and brain games will tire a puppy more than exercise which can just increase adrenalin levels and actually make the puppy more hyper and then you think it needs more exercise and the cycle continues.
The first consideration with puppy exercise is the growth plates. They are soft areas that sit at the ends of the long bones in puppies and young dogs. They contain rapidly dividing cells that allow bones to become longer until the end of puberty. Growth plates gradually thin as hormonal changes approaching puberty signal the growth plates to close. In puppies, this closure is normally completed by approximately 18 months old. As ligaments and tendons may be stronger than the growth plates and so they can actually cause damage to the growth plate.
However puppies do need exercise to develop just not excessive exercise and not endurance as their cardiovascular system is not fully developed.
So free play is great, if he flops then tries to get going again intervene and encourage rest. Not too much lead walking just enough for a burst of training but no long lead walks.
Absolutely no jumping on furniture or jumping off furniture (It can cause horrendous back injuries).
He sounds great 