I would not give up on driving him just yet (though I would keep that in my mind).
It is possible -- especially since he acts fine anywhere BUT your car -- that the issue is he's hungry and tired. This is immediately after school. He likely has not eaten since lunch, or if he buys school lunch he might hate it and eat too little, or his mom might not be packing him enough lunch if she packs it. It really is not all unusual for young kids to have rough afternoons immediately after school due mostly to being over-tired and hungry. He's five, not 15, and probably doesn't even realize he's tired and hungry; he's just mad at the world and doesn't know why.
Yes, do lay down the law with him before he enters your car (I hope you walk to the school to get the kids rather than having them leap into the car in a "pickup line") but also -- talk to his mom today and tell her you have noticed that he is cranky and argumentative right after school when you know he is well-behaved otherwise. Tell her you plan to bring both kids a snack to eat as soon as they get in the car. She can provide it or you can. The snack does two things: It occupies them for a few moments and it gives them a needed boost. Protein snacks like cheese sticks are excellent for this. Find out what he eats, though -- you don't want to make him fussier by offering him a cheese stick if he loathes cheese. This is why his mom needs to be involved here.
When a kid who is otherwise fine has sudden behavior issues that take place at the same time and in the same location consistently -- the issue may not be that he's a "devil spawn" as someone else posted. The issue may be that his blood sugar is crashing. That makes even an adult mad as a hornet.
I'm not saying this is solely a physical issue, or that he does not have any behavior issues. But it's worth talking to the mom, telling her that his immediate after-school behavior seems different from what you see otherwise, and telling her that you want to try an in-car snack for both kids and see if that helps.
Give that some time and then if he still cannot pull it together, you need to ask the parents to talk to him about "car manners" and tell him that when he is in your car, YOU are the boss of him. He also is just starting K, a time when many kids who are not used to obeying ANY adult except mom or dad realize that they are being told to do things and obey new adults, namely their teachers; he may be lashing out at you because you're yet another new adult telling him you are in charge. That is not an excuse! But it is another possible explanation. His parents need to be the ones to tell him that this is the way things are -- in school, the teacher is the one he must listen to and obey; and in your car, you are the one who's in charge.
But I'd go with the snack strategy first.