It's important to note that the new update will reduce the overall size of your Modern Warfare/Warzone files, but you will need the required space on your hard drive before this happens.
So what is the size of this new update?
Season 5 PS4 Update Size
The update size for Season 5 is 33.6 GB on PlayStation 4.
You can find out how to pre-load the update early here.
Season 5 Xbox One Update Size
The Update size for Season 5 is 49.8 GB on Xbox One.
Season 5 PC Update Size
The Update size for Season 5 is 54.2 GB on PC.