Is it crazy to date your ex-wife's first cousin five years after the divorce?

That does depend on many things - how old is the cousin? How close is she to your ex-wife? How amicable was the divorce? You are your own person now and perfectly free to date anyone, but take into account your wife's first cousin may not see it this way, and neither might your ex-wife. If you really like this woman then go for it, but think if through seriously first.