About the fresh broccoli, it lasts a maximum for 1-2 days at the normal temperature. But the cooked broccoli doesn't last more than 2 hours at room temperature. However, the duration is not for the fridge or freezer. You don't have to care about both the cooked and raw broccoli for 3-5 days. They perfectly remain well for the 3-5 days in the fridge. Conversely, the freezer keeps them fresh for three months or more when your storing process is okay.