Bear in mind many of her class mates may not be five yet, so think about those 4 years old you'll have to be in charge of. Yes some parents can't/won't stay and you'll be in charge of these children.
Basically kids this age tend to want to run around, eat lots of cake and get a party bag full of sweets and tat.
theme park and horse ridig seems to be un-necesarily complicated -
what they wear (some little girl will turn up in a party dress i bet you)
then there's the liability/insuance forms the horseriding will require
what if some parents dont stay (yes even at this age some wont stay, especially of they have siblings who aren't invited)
and what if some children have never been horseriding and find it scary or refuse to get on. You'll still have paid out for them.
Theme park again complicated. To may children going in different directions, especially ones you don't know. Or are you paying for their parents to come in to supervise them too? Again issue for those with siblings not invited who need to go/bring them too.
Plus you'll still be spending out on a cake and party bags presumably... And you say you are trying to save money!?
Choose something easier and cheaper perhaps? How about a pottery painting place if you only have a few? Or yes definitely hire a hall and play pass the parcel and other fun for five year old games. That way you can invite the whole class and not worry about the extra cost (too much). You'll need squash, cakes, crisps and sweets to feed them, some music (you can hire a dj if you want but not necessary), some games to keep them amused. Girls like fancy dress but boys don't always.
Good luck with whatever you decide to do.