I think with all these things you have to teach your child very carefully how to do it, and do a kind of risk analysis depending on the probability of injury, circumstances in the kitchen, child's personal manual dexterity and self-preservation instinct, and so on.
I used to work in a Montessori nursery many moons ago, and our kids did things like chop up apple, clean little pieces of glass and sweep up properly from the age of two. Obviously we kept a close eye on them, but they were perfectly capable. That encouraged me to help children do a bit more for themselves than I might have considered appropriate previously.
On holiday last summer we shared a villa with some friends, and their younger daughter helped me peel and chop up the apple for a dessert I was making, with a proper peeler and knife. She was 7. Now I was watching her like a hawk because I am not daft, but her dad was incredibly nervous. I had explained to her about knife safety and I could tell she had the dexterity to do it (I have known her since she was born), so I explained that to him, and he just about let her carry on, although he didn't like it because she was his little baby (of course). She loved it though, and did an excellent job. However my DS2 is absolutely not allowed to do this because he has dyspraxia and is relatively cack-handed. He is just not ready.
I came across this film which is a very interesting debate about what is possible for young children in terms of dangerous things.
www.ted.com/index.php/talks/gever_tulley_on_5_dangerous_things_for_kids.html
Anyway, having said all of that, I would not let a five year old use a kettle because they can't lift heavy weights and liquids reliably at that age, and therefore the potential for real injury is huge - a lifetime of skin grafts. With a small kitchen knife under close supervision the worst case scenario would be a few tears and stitches, and you would be going it some to do that much damage, tbh. It's all relative.