Basically.. you have the best 5 card hand you can make with your 7 cards (2 hole card+ 5 community). So if the best 5 card hand is your K + the board, then your kickers don't come into play.

K5 vs K4 when both of you hit your K will usually be a split pot. However if one has KJ and you have K4 and there is a flopped K, then you'll most likely lose due to the kicker.

Only way to tie that would be a board of like AAKQ2.. then the best hand for both is AAKKQ. If the board however is AAK52, then his best hand is AAKKJ and yours is AAKK5, hence you lose. (note your kicker doesn't even appear in the best hand here because it is so low)