Readless on this particular cat - he had just sat down as you can see by his stack size.
I am not too worried about this board...how much can be extracted from my opponent on the end? I was figuring $4-5 or allin river bluff (after reviewing the hand).
Does one bet more on the turn as well given opponents likely range? I don't want to scare him away.

Party Poker No-Limit Hold'em, $ BB (10 handed) FTR converter on zerodivide.cx

SB ($7.90)
BB ($25)
UTG ($28.15)
UTG+1 ($9.50)
UTG+2 ($45.30)
MP1 ($23.25)
MP2 ($5.70)
MP3 ($31.83)
CO ($5.80)
Hero ($26.05)

Preflop: Hero is Button with K, K. SB posts a blind of $0.10.
4 folds, MP2 calls $0.25, MP3 calls $0.25, 1 fold, Hero raises to $1.5, 1 fold, BB calls $1.25, MP2 calls $1.25, MP3 folds.

Flop: ($4.85) 5, 5, 3 (3 players)
BB checks, MP2 checks, Hero bets $3, BB calls $3, MP2 folds.

Turn: ($10.85) 2 (2 players)
BB checks, Hero bets $4, BB calls $4.

River: ($18.85) 3 (2 players)
BB checks, Hero checks.

Final Pot: $18.85

Results and further comments in white below:
BB has 8s 8h (two pair, eights and fives).
Hero has Ks Kc (two pair, kings and fives).
Outcome: Hero wins $18.85.

Oh - and before you make too much fun of me for pussing out altogether (still kicking myself in the nuts which is quite uncomfortable), I had lost a recent hand with KK to a slowplay (didn't overpay) - so I played it overly safe in case he chased the gutshot and lost value --- leak!