It depends on how they do it, even at the age of 5.
Running up to your mum and jumping for joy because you got a teacher's star for your reading is fine and hurts noone.
Telling your little friend that "I can read level 5 and you're only on level 2, because you're not so clever" can, if you are unlucky, undermine little friend's confidence for good.
Telling your friend's mum how well you are doing in your friend's hearing can also be a bit undermining.
Ds had a friend like this (I can do x and you can't; I am on level y and you're only on level z because you're not very clever). It was a constant drip, drip, drip.
I don't actually believe this 5 yo boy was a deliberate bully; he was just innocently pleased that he was cleverer than his friend and nobody had told him the rules for these social engagements.
After a few months at school we noticed that ds was beginning to say things like "I am not very clever", "I can't read like the others". After a few more months the teacher was mentioning that ds didn't seem to engage very well in class. And the less confident he got, the less he tried and the more he dropped behind.
It has taken him until Yr 8 to regain his confidence and realise that maybe he can learn things too.