Hi Emz,
I am really sorry to hear that. This is without a doubt, the builders problem, to put this right.
You gave him specific measurements, that are absolutely crucial, because of the size of the structure, that's going to go on it.
He will either have to get a large angle grinder cutter, with a blade able to cut through concrete and remove 5cm, from it, or he will have to break that base up and redo it, either way, it's his responsibility to do this.
I assume that you have not paid him for this yet, or if you have paid part, you want the work completed, as per the measurements given to him, before you pay the balance.
This causes a great deal of stress, when things like this go wrong , really not what you need at all.
Is there anyway, that you could get someone from the company, that's supplying the new garage, to come and have a look and see if there is a way round fitting it to that base, at the builders expense, obviously.
I really hope that you can get this resolved, there is no excuse for what he has done. xx