Board and card games are a great activity idea. I think that 5 is old enough to be able to handle moderately complicated rules, but (more importantly) old enough to keep track of what rules apply to which game. Indeed, the variation of many new games probably helps memory and strategy skills, since she has to keep things straight!
The trick is to balance the new information against making things too repetitive. Too many new games at once is confusing for anybody; playing chess (fairly complex) for many days in a row to practice could potentially get boring and frustrating (I hated chess as a child!). I don't think there is any firm guideline that would really work, just keep an eye on how well she's understanding things and how much fun she seems to be having.
(As a side note: in my experience, when a five-year-old starts to cheat or simply ignore rules, she's bored or frustrated. That's a good sign it's time to switch games...)