since your daughter is only 5 and not 15 your choice would be different and more age appropriate. i started my sons out at 5 years with a small daisey 22 cal single shot bolt action rifle. i think a single shot is important for safety reasons and to develop accuracy. the daisy rifle we had had a plastic stock, it looked like a normal wooden rifle but it had a button in the stock that would allow the but plate to extend as the child grew. i feel that a single shot rifle is important for a first time young shooter to develop good shooting skills and habits. the daisy rifle had iron sights, again every shooter should start with the basics and develop their skills before they advance to scopes, red dots etc.
the daisy rifle we had was a well thought out rifle for a first time shooter, i dont know if they are still available. the features it had that i thought were good for a first time shooter are:
small size and light weight for a child.
bolt action single shot for safety and developing shooting skills
iron sights for learing to be accurate
expanding stock to grow with the child
add to that good adult supervision
these are features i would recomend in a childs first gun. try to find a gun with as many of these features that you can.
things i would avoid.
buying too much gun (length, weight, ammo capacity, semi auto) for the child even if it is a good price.
i would avoid semi autos of any kind at her age.
i would also avoid any multiple shot rifle. lever actions, tube or magazine feed rifles are all great but they should be something the child should graduate to at a later age.
i am sure there are many brands of rifles out there that meet my recomendations. i think that if you find one for your child it will pay big benifits later in skill, accuracy and safety.
Waltzes with woofs