DS had a Stentor one, which the shop had "improved" - I think they changed the strings and the bridge to make the sound better. But he started with a second-hand one of those, and didn't get a new one till he got to full size. Second hand ones are certainly just as good, specially when you think how quickly they outgrow the small sizes.
I would get a cheap one. SHe is 5 years old. The instrument (however careful she is) is likely to have an accident at some point. She may well give up. It's really not worth the money at this stage as the best violin in the world won't really make them better.
Save the money up and get her a really good one when she gets to teenage years if she still keeps it up.
IME as well, a violin (as any instrument) should be chosen by the player and for how it fits/feels to the player, not what 'make' it is. Your dd won't be able to tell this early as she is so young and only just started.
BRing back the bright orange school owned instruments!
If you have a violin shop you can get to reasonably well, you may find that they will do part-exchange on the smaller ones as you move up, which can be less hassle than selling it yourself. After the first one, DS's were always returned to the shop when he went up a size, and they took the value off the price of the next one.
DD (7y) has a stentor conservatoire violin (approx £175). She has been playing for 18m and up until a few months ago had been playing a super cheap Chinese violin (free from School). We can definitely hear the difference and so can she, although she is only Grade 2 standard. The shop we bought from will do part-ex when she needs to move-up a size so the cost seemed reasonable.
I am minded to go for the cheaper Stentor for a number of the reasons stated. Difficulty is that, in keeping with what Armadillo has said, she likes the Suzuki that we rent, is comfortable with it and insists that it's hers!
If she is having lessons through school then ask if they can supply instruments. Herts Music Service offer a range of instruments for pupils of all standards and it's cheaper than buying from a shop as they are VAT free. I'm sure other counties must do the same.