Here are a couple of pics of one of four bows I'm working on right now.
Made of one 48" piece of red oak measureing 1.5" wide and about 3/16th thick ($2.20) with the handle glued up from one piece of poplar the same size but about 18 inches long ($0.88). This one is backed with rawhide, but one of the others backed with paper bag and wood glue is much easier to apply and just as effective. Limbs are cut to "pyramid" shape with the tips being about 3/16th wide. By cutting to pyramid there is no other tillering involved. Time (except for drying glue) is about 1.5 to 2 hours per bow.
For a five year old it should draw about 10# depending on her size. Bow will grow with her! I drew this one back to 25" on a tillering stick and it was not overdrawn.
I have six grandkids so these are meant to be around the house for them to use when they visit.
So, that's a inexpensive DIY solution and the kids like to participate in the building part. Nothing like "made by dad".