I think they will find it difficult to budget as they get older if you only give them £5 but then you are paying for lots of other things on top of this.
My 14 year old gets £50 per month. He bought his own phone from birthday money / savings and he has a giff gaff sim which auto renews each month which he pays himself. He has a bank account with a debit card so has to budget for the phone money coming out each month. He pays his own way if going out to the cinema, into town with friends etc. He saves up for specific things he wants. I buy his basic clothing and any expensive designer stuff he gets himself. I will buy him the odd thing for Birthdays / Christmas.
He has his own amazon account which his debit card is linked to. The only rule we have is that he shows me what he is buying so I can check that he is getting it from a decent seller with good reviews etc.
The same goes for his xbox account it is his card linked to that so it comes straight from his account when he wants to buy something.
I also pay his school lunches which work out at around £3 a day. I just stick £50 on the cashless catering system at the start of the month and he knows if it is all gone before the end of the month he has to pay for lunch himself.
I pay bus fares to school but not for going into town with mates etc.
On the whole he is very good with money and I never tell him he can't buy something with his own money as it is his to spend as he wishes.
My 10 year old gets £5 a week at the moment as he is younger and does not have the same social activities to pay for. When he starts high school I will do the same as I have for his brother.
I really think that giving children the responsibility to budget their own finances sets them up well for the future.