All of the answers so far seem to focus on uniforms in general, but not on your specific case. While there are arguments for dress codes, pro and against, in upper levels I think few, if any, apply to a 5 year old. They aren't at the point where they feel they are competing in clothing, they rarely notice what others wear, nor is there a substantial difference in costs between 'cheap' and 'expensive' clothes for 5 year old. At the same time, since mommy usually still picks her clothes for her, she can't really express individuality. Basically the majority of answers do not apply because children this young are not at the point where they are aware of clothing choices of themselves or others enough to play a significant affect on their development or success in schools.
My honest suspicion for why your school has a dress code is immitation. Many private schools, including some of the more presteigious and expensive, have dress codes for older children, for the reasons addressed in other answers. Since your school is trying to be a prestegious pre-school it's attempting to mimick those tropes associated with such schools. This can give them the feel of these schools, maybe even convince parents their more prestigious because they are 'fancy' enough to require a dress code.
Alternatively depending on what ages this school covers it may have older kids in higher grades where the dress code matters more and simply apply the dress code equally to all grades.
Either case the affect is the same, it's not that 5-year-olds need a dress code, it's that the sort of school they want to be requires older kids to have dress codes, so they apply it from the start.
Personally, I'm opposed to a dress code for such a young child, though I think it ultimately isn't a significant factor. My primary concern is simply logistical, you're forced to buy more clothes to have enough that fit their standards for a week, and have to apply extra logistical effort into making sure that you not only have a clean shirt, but the right type of clean shirt, for your daughter. It's not that difficult, but it's a hassle and expense for you that offers no benefit.
Furthermore, while I feel the affect on individuality is less important at this age then with older children I still encourage kids to express themselves with decisions at young ages, and some choice over clothes is a good low cost decision, a starting step for children to feel they have agency and choice at a young age that leads towards more decision making later, and the dress code is limiting this to a degree.
I'd be more understanding if this school goes all the way up to 5/6 grade, instead of being limited to preschool and/or kindergarten, as instituting a dress code early avoids the need to transition children to the dress code at an older age (when it's more relevant) after they have already gotten use to having more choice.
Ultimately though, the difference is pretty minor. Go to whatever school is best to your daughter and juts go along with the dress code they have if they have one. Your not going to see a significant difference in development or well-being either way so no need to worry about it too much.