i do not know if a 5 yr old will be permitted to participate.
i recommend leponderosa or gold mine ranch.
there are a few others, but i have no first hand knowledge of their operation as of recently.
i have ridden within the past couple of yrs numerous times with the 2 that i mentioned.
check out this thread
andrea Horse back riding
My honest opinion is to skip the horseback riding. We went horseback riding in Aruba and when we were going through customs once they found out they wanted the clothing and shoes we wore and they pulled us aside and sprayed down the items and put them in a white trashbag. All this hassle from riding an unruly horse is just not worth it. Just my 2 cents, hope it helps.