Understandable to get confused in this situation, it's hard. You have this super strong hand preflop and now the flop comes down and gives you nothing.

For me I'm probably flatting the 3bet preflop, checking the flop. Preflop 4bet is ok but I'm going to lean towards flatting when it's AKo as opposed to suited. (this could be wrong idk) -- On flop we don't have a value hand and we have basically no draws. If they bet small I can see calling one street, but facing a 75+% bet I'm just folding.

Most players especially at NL5 aren't going to c-bet into you after you show a lot of preflop aggression unless they have value. Given that you 4bet preflop, you can pretty safely check and then fold to any bet above 60-75% sizing. Lower than that I feel comfy with calling in case they have some worse hand, basically suited Ax Kx Qx hands that miss the flop is the range we are hoping to beat if we call.

Problem here is so much of their range hits the flop -- mid-range suited connectors, AJ, KJ, QJ, A8, A7, T9o, pocket pairs 7 and up, etc etc, it's just not a great spot to be in.

Overall, don't be sad to fold strong preflop hands when they just miss the flop. Just having overcards isn't really worth defending or bluffing over when the stacks are deep.

Been thinking about this preflop spot recently and relying to my solver and some thoughts of others: Jamming AI pre with Ako might be a solid option to avoid this spot.
Opened a thread "Avoiding 4bet pots" some days ago, where we discussed about that topic:

https://www.runitonce.com/nlhe/avoiding-4bet-pots/

I honestly think the way you played this is pretty much perfect. I don't see any problem. As for getting run over out of position, I agree with RaoulFlush . Jamming might be a good option. I don't necessarily like just flatting a 3bet with such a strong hand against an abhorrently weak player pool though. Your bet sizing was pretty spot on, I think the only other thing to mention is - If this player is looser, this flop should be pretty +EV for a more open 4bet calling range. Your 4betting range is going to be like AQs+/JJ+. The larger majority of that is going to be like AK/AQs, so I think an opponent is going to call any QQ/AJ, sets obvious, and all the other things quixoticflux888 mentioned. This board in particular I'm guessing you're going to be betting at a high frequency regardless, but maybe just be more aware if you're facing a looser opponent on boards like this, and be more willing to give up if you don't have the goods. I would say don't just think about this spot when you have AK, think about this spot considering your whole range, and see how all the different hands play out. You're probably actually printing here with your whole range, AK is just a portion of that :)

This thread is why I pay my subscription. What a good hand to share!

e-mal says

"I would say don't just think about this spot when you have AK, think about this spot considering your whole range, and see how all the different hands play out. You're probably actually printing here with your whole range"

and I think that is brilliant advice

Just to add my own 2 cents, if you only every bet AA no-one calls - you need to have weaker hands so that Villain thinks they can win sometimes. AK is working as a semi-bluff for you here and when it misses that's ok - in other situations it wins money when they fold to the 3 bet or when you hit an A or a K, or by blocking their range and making them play with a capped. It can also win at showdown so when it misses it's sometimes worth playing it as a check-call

You played the hand the same as I would most of the time, you can consider doing something different preflop but 4b should be the normal play. If you have a diamond you can reasonably jam the turn (I definitely wouldn't ch/jam at these stack depths), but I would be reluctant at 5nl.

If the turn is blank I am still ch/f turn a lot against unknown at 5nl. If you are worried about being exploited then you would ch JJ or AA on a blank turn sometimes to induce, as if they ch back you can jam the river anyway.