You're the mum, she is 5. Tell her what she needs to wear to be warm and comfortable and that's that.
I know its easier said than done, I have a 6yo DD who likes to try on 7 different outfits and leave them all over her floor. It got to the stage where I removed all her clothes except for dressing up outfits and put them in my wardrobe, so she had to come and ask for new clothes when she needed them! She's since 'earned them back' but I still have the final word on what she wears for school and elsewhere.
If you want DD to have some choice perhaps give her the option of 'blue tights or grey' or put the socks away until March and tell her tights/trousers are for winter. WRT the cardigans I would say tough, they are the ones I have bought, they are the ones you wear, its not up for discussion. Perhaps try a sticker chart, add one for each day she gets dressed without an argument and at the end she gets some new hair clips or a winter hat or something?
Its a shame girls have so many variations in a way - with boys its so simple, t-shirt, jumper, trousers. Girls can choose trousers, skirts, pinafores, summer dresses (choice of 2 colours), cardigans or jumpers - it makes it seem that the way they look is more important, whereas really its a uniform FFS, they should all wear the same and get on with learning.
I would fully support my school if they said that all girls had to wear trousers, t-shirt and a jumper just like the boys.