With all due respect, I don't think this parent is going to let the decision solely rest with her five year old. At the same time, if the child doesn't want the CI, that should be taken into consideration; as should a desire to have one. A child of her age is perfectly capable of voicing an opinion on this.
After all, it is the CHILD who will be wearing the CI; not the parent. If the child is old enough to articulate how they feel, I feel it is a parent's duty to include that child in the decision making process.
And, as for the phrasing of "being put to sleep". That's no big deal, Cloggy. A child doesn't understand any euphemisms of euthanasia. They would only understand it to mean what the parent intends for it to mean for them.