Indeed you didn't have top pair, you had a set which is much better. And then a full house which is better still.
There is 1 way to make KK (for KKKKT) left in the deck. There are 2 for KT (for KKKTT), 6 for K6 (KKK66) and 6 again for K4 (KKK44). That's all that beats your TT for TTTKK.
Now here are the figures for some hands you beat:
Kx (for KKKTx): 8 each
44 (for 444KK): 3
66 (for 666KK): 3
AA (for AAKKT): 6
JQ (for a busted straight draw): 16
These are the frequencies based on the definite information available to us: the cards on the board and in our hand. As poker players we use judgement to mould these into an approximation of the real probabilities of our opponent holding those hands and seek to take the action which our opponent responds to in ways that produce the most profitable average.
K6 and K4 are folded preflop by most players even at NL5, so they get reduced weight. KK is raised most by players even at NL5, so the same applies. The same is true for AA.
Without knowing the player we can't say much about the other candidates from the preflop action (calling the min raise means nothing more than that there was no intention to limp/reraise, again speaking against KK/AA), but the flop action tells us more.
When the preflop raiser bets on the flop we can't infer much about his hand without further information. Many players, ourselves included, do this almost regardless of our hand as long as there aren't too many opponents. The size (half pot) is also suggestive of it being one of these "continuation bets", we can blame or thank Dan Harrington for that.
This bet is raised by the minimum. Raising a continuation bet, especially in a pot which isn't heads up, usually means that the raiser has caught part of the flop. A player who does this with JQ is raising as a semi-bluff (he is likely behind now and would like to win the pot immediately but there are 8 cards in the deck which will give him the nuts if called and he can still win... win a much larger pot than the current one even because he has disguised his draw!) while a player who does this with 44, KT, down to maybe Kx or Tx depending on how fishy the player is intends his raise to be for value. He hopes that he will be called because he thinks he's the favourite.
...now that's not very helpful, so here's something which is: most players want top pair or better or a draw at least equivalent to a gut shot straight draw (the fish want this, better players want open ended ones) to continue beyond the flop. Kx is very, very likely if many Kx get here in the first place. Suited Kx in particular does, beginners overestimate how often they make flushes and love to play suited aces, suited kings, and in the worst cases any suited T or better or even any two suited. Off suit Kx is often played by weak players too, less than off suit Ax but pretty often. KT+ (suited or unsuited) is played in this position by virtually all players.
The size of the raise doesn't necessarily mean much at NL5 where almost everyone's consistently underbetting or overbetting, so we'll not go into that. It's a play which practically guarantees a call, is cheap and doesn't bloat the pot, view that as you will. It depends on the psychology of the player in question.
The bet on the turn practically rules out QJ, which was a possibility on the flop, from both players' hands (not that the big blind is relevant any more). With two callers and a good draw, any remotely decent player (the NL5 factor keeps biting us when trying to make rational assessments of play, but never mind) would not bet again when the high card pairs, he would instead check behind. Kx would probably bet, as betting your good but non-nut made hands is standard play, 44, K4 or KT might check behind in a poorly conceived slow play (so terribly common in the micro limits) as they have a virtual lock on the pot (yes, even 44, which you beat), KK likely would as he would now know that nobody has a K and desperately hopes that one of you will catch up a little on the river.
The turn bet is unusually small, which again at NL5... but this is a little more reliable than the raise, it'll tend to either be a cheap shot at the pot with a hand of little value or a value bet with a very good hand.
(Checking on the turn is okay because of the high likelihood of Kx, the low likelihood of anything else paying you and the possibility of other hands bluffing.)
...that was a bit rambling, and not all correct, and all I initially meant to do was point out how relatively unlikely it was that you were beaten and relatively likely that you were getting called by a worse hand. Maybe someone can extract the sense from here.
Perhaps what you should take from this is that you really don't know that your opponent has one of the four hands that beat you, which can be made in 15 ways total (6 of which are 66, which is unlikely to get here). You really, really don't know. Nobody knows what their opponent is holding, especially if the opponent's playing style is unknown; sometimes they guess and sometime's they're right, but more often they're wrong, so what we have to say at the table is "He could have a whole bunch of holdings but I think this lot are more likely than these ones given the number of ways to make them and the action so far. If I bet, maybe he calls or folds with these holdings (mainly draws and weak made hands), or calls or raises with these (mainly draws, strong made hands or air looking to raise on another street if he calls), or raises or folds with these (draws and air). What kind of player is he and which will he tend towards for which classes of hand?"
...god, I'm rambling again. Someone stop me.
NEVER EVER minimum bet/raise - remember this rule and use it!
