Fencer: Well i hope someone can back me up on it. (since I'm pretty sure, but I know I'm not an expert card player and could be missing something)
That is how I have always played - the cards of the table of "shared". So using those 5 cards, and the 2 in my hand - you make the best 5 card hand. (and each other player does the same)
Best 5 card hand wins. So if you have a pair, you take the pair & the next 3 highest cards and ignore the other 2 to make the best 5 card hand........I've never worried about what it was called (kicker and such).