Sadly you did the right thing my friend...you say you have a hard time looking your 5 year old in the eye right now ....imagine having to look at that 5 year old if the dog accidently disfigured that precious face. I had to put one down because he killed the family cat , I wouldn't hesitate to put one down for hurting a child..seems harsh , but it's for the best.
Time heals all wounds and children are number one and relie on us to protect them from harm , which is what you did..