I think he played his hand completely fine.
His flop bet was a little large, but they were quite deep, so I don't mind. He has a very strong hand and will be bluffing this flop a ton. It makes a lot of sense to include value in his range as well.
Turn check is a little strange, but you have to realise hero will be bluffing the flop a lot. Protecting his check range every once in a while with a strong king in this spot makes a lot of sense.
River bet is fine as well. You can get value with your strong kings and mix in some good bluffs. Getting raised is very tricky, but his call is completely fine. Out of all the kings he has in his range, AK is obviously the strongest one. Hero doesn't really have a 5, so he is capped. If he is folding AK he is folding 100% of his range. Besides, the only thing villain is really representing is pocket 5s and 6s. Folding AK is exploitable. He played his hand very well.
You can make an argument for calling some of your AK's and folding others. There is a small chance villain had a backdoor flush draw on the flop and now turned it into a bluff. There wasn't a spade on the flop so AsKs is the only combination perfect for a call. AsKs HAS to be in your calling range. I would never fold AK here, but you have to call with all of your AK's containing at least one spade.