First, if you are going to teach your children how to shoot a rifle you need to buy a child size weapon....shorter stock, lighter components and usually a single shot.
Second, the weapon needs to be secured safely. Evidently these people thought they did with a trigger lock safety but left a cartridge in the weapon. A mistake with tragic consequences.....
I taught all four of my children to shoot beginning at 5 years old, always under extremely close supervision and the weapons (when not being transported or used) are locked in a gun safe.
Gun safety and weapons training should begin at an early age.
These parents (from other reports) were good parents,loved their children and made a tragic mistake.
No doubt they were good parents, very sad story.
Personally I do not think I would put a firearm in the hands of a child before 11.
If a child was to be trained prior to that, it would be with a bb gun.
5 seems much too early to me for bullets. I do not think a child has the capacity to understand the consequences of bullets at that time.