imo children should do one structured sport and one art activity per week.
Or, considering we're talking about a five year old here, perhaps he can just run around playing games with his friends in the playground and get his crayons or play-doh out when he feels like it?
I personally don't think a six-year-old needs to do an organised sport or physical activity. Important for him to be active, of course, but he can be active by riding a bike, climbing a tree, building a camp in the garden, throwing a ball against a wall, dancing around his bedroom to his favourite music or any number of other things, in addition to his swimming lessons. And I'm pretty sure he'll be learning things like teamwork and structure from his PE sessions at school.
Like others have said, if you think he isn't getting enough variety from school and his normal play, then how about something like Beavers or Cubs or whatever? Then he'd do a mix of activities, learn teamwork and other skills, and have the chance to try out different things. But he'd probably also get to do some badges that play to his existing strengths and interests too, so it's a good mix.
I didn't like organised sports when I was a kid at all, but I was more than happy to play really active, physical games at Brownies!