AT+ probably , weird villain does not shove , depends on population if you want to hero fold here

I think you are beating nothing in his value range. Jx isn't likely to bet river. It's tempting to call for that price but he has to have enough complete whiffs. 87cc, KQcc, QTcc can bet here but his missed draw range is going to be pretty thin. I don't really see him value betting Jxcc when AK, AQ, AJ are easily still in your range on this river.
It's close but I think it's a fold.

Fold Turn itself and if you decide to call the turn river is also call then. 5h doesn't change the board much.

You probably get here with A5, maybe 56s and then AT+, sometimes AA. Bluffcatcher wise, A8 is quite good as you don't block any of his bluffs like the broadways and clubs and you block some of his value combos like 78, two pair and better Ax. Would also expect sets to raise a decent amount of the time on the flop.

I don't have any data to back up that this line is underbluffed and ranges are probably quite wide here so as a default would call unless you have population reads or reads on villain to make an exploitative fold.

Seems like a very clear call to me, clubs miss and since you're probably perceived to play most/all KK/QQ/Jx this way, villain could easily go as wide as weaker Ax for value on the river, especially for this size. A-blocker is also very relevant, there's probably like 5% difference in terms of equity between KK and A8.

I'm pretty sure this is a call. First, As is very important, because ur flop cbet forces folds some weaker A highs with no backdoor flush draw, for example, Ac8c probably has to be a fold whereas As8s is a clear call, so villian has much fewer Ax combos on the river. Also, u block a lot of the Ax suited two pair combos with As. Secondly, u do have the blocker to a straight, which is basically one combo, but still relevant. Also, u unblock his flop floats, high card with spades around the J, or any missed club draws. However, I do think turn should be a bet because of the equity increase for OOP on the A turn, ur turn sizing should probably be split into an overbet and 1/3 pot range, and A8 should probably be in 1/3 pot range at a very high frequency. It should probably be played as 1/3 pot turn, and X/C this river.