k ranges like this say
CO:22+,A2s+,K6s+,Q7s+,J8s+,T8s+,97s+,86s+,76s,65s,54s,A9o+,KTo+,QTo+,JTo
BU: TT-22, AQs-A6s, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 76s, 65s, AQo-ATo, KJo+
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Board: 5C8H6S
Equity Win Tie
CO 47.63% 45.53% 2.09% { 22+, A2s+, K6s+, Q7s+, J8s+, T8s+, 97s+, 86s+, 76s, 65s, 54s, A9o+, KTo+, QTo+, JTo }
BU 52.37% 50.28% 2.09% { TT-22, AQs-A6s, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 76s, 65s, AQo-ATo, KJo+ }
BU distribution

CO distribution:

He has slight range advantage on this board so I guess it's okay to check fold a decent amount.
I wouldn't overdo it tho cause he seems to have wide stats+gap between PFR and VPIP wide enough to call alot OTB and exploit you if you just CF too much. I think you are pretty much forced to cbet a good chunk of your overcards and barrel a decent amount of em accordingly. I'm assuming AJ will be one of the better ones? I'm guessing you won't realize much of your high card equity but with the better top pair outs this hand is better than all your QJ KQ wo backdoors that you can check fold here, so at first glance I think we have to cbet this kinda. not sure about cc but we still have AK AQ from Ahighs. and I assume you do want to protect your checking range vs this guy too.
we have a discussion going about range assymetry which is the case (kinda; the board isn't as bad for you as you thought as you can see most likely) here, feel free to pitch in - there's a COvBU spot too in the OP. it might be okay to cf even this hand, but i think the board would have to favour his range more
https://forums.pokerstrategy.com/forum/thread.php?threadid=328501