Go for it OP. From the minute your DS walks into the school on his first days his poor benighted form teacher will be thinking 'Oh god, this is the kid with the mother who is going to be a massive pain in the arse! As if I didn't have enough to deal with .'
I was at a grammar school in the 1970s, the fashion was for ridiculous platform shoes, so of course we were limited to 2 inch heels. Do you know who the coolest girl in the school was? The girl who came in flat as a pancake Doc Martens! How to follow the rules and stand out at the same time. The whole school went, 'Why didn't I think of that?'
As for people saying 5 year olds don't care, some of them will have older siblings in the school and they will share a playground.
Do let us know how your little darling gets on in his girls shorts btw.