In many cases, you will want to consume properly stored leftovers within five days of storing them in your fridge. The golden rule is to eat pre-cooked leftovers within three days of storing, ensuring that they are fully reheated before consuming to mitigate the risk of consuming dangerous bacteria responsible for causing food poisoning.
One exception to this rule is things like sauces. Cranberry or apple sauce, for instance, can usually be stored in an air-tight container for seven to ten days in the fridge, so long as there are no other food contaminants in them.