So after a few hours of trying some other stuff, I devised a way of making this game have more "random" cards. But using this method, the cards must be "shuffled" after every hand. Here's how I am doing it right now.

Pick five cards from "random", making sure they're all different. Then, depending on what the player selects, get 0-5 more "random" cards, again, making sure they're different from the ones already dealt.
Repeat process over and over again, once for every hand. Should I make it so that once all 52 cards are used, the game "shuffles" them all, or keep doing it the way I am now? Because tracking 52 individual cards using C would be really hard. Wouldn't I have to make cardsdealt[52]? A variation of my process of getting "random" cards is also used in Blackjack.

And here I was just proud of my new way of getting "random" numbers so that it wasn't dealing straights for me a whole bunch.