Is Ke6 a legal move in this position?

Hi all! Hope this is the right place to ask this question. If not, please let me know and I'd delete the post.

So, my kid and wife were playing and we had this position.

Black to move. Like the title said, is Ke5 a legal move while the white knight is pinned?

Edit: typo. I mean Ke5.

Yeah, that's actually what I thought. But the kid wanted a convincing reason but I genuinely don't know why it's illegal.

A king can’t walk into check. You could explain that if whichever side was able to capture the king first, then white would win because he would capture first.

Thank you! That sounds persuasive to me!

The game ends in checkmate whenever a king is put into a position where no matter what the other player does, that king will be captured on the next turn.
Let us assume that Ke5 was possible. Then, white would play Nxe5, capturing the black king. It doesn't matter that white's own king is hanging, because black no longer has a king
A way to explain it to your child is this way;
Think of the king as the 'brain' behind the pieces. If the brain is threatened, then it is crucial that all other idea's be interrupted to defend the brain. If the brain is lost, there's no directions given to the army anymore.
Therefore, the brain can NEVER walk into danger. And if the brain is put in a position where it is in inescapable danger, the game ends.

No. From the laws of chess:

3.1.3 A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack.

Whoa, I don't even know there are systematic laws for chess. Think it should have though. Today I learned!

I think you mean ke5