It is very very hard for your manager to accept that he/she was pushed by you,then providing you counter offer.
As manager, he has budget and pressue from CEO or his boss. He won't think you deserve that marketting value even though you got offer from other company. Firstly he thought you made him trouble and made him lose face. Seconding, nobody wants to be pushed. Third, he knew you were trying to move and he would have felt risk and prepare a backup.
After I accept counter offer, my manager was more emotional than before. He tried to take care of me better for keeping me stay, at the same time he was mad at me at his bottom of mind.
And for 5k higher counter offer, by my current experience, it doesn't deserve you stay at old company.
If me, I would go.