I am using a Raspberry Pi Zero W and the picam v2 to record videos continuously for several days. Files recorded are only 5-minute long. Can I save files on the SD card directly, or should I use an external USB drive? I am worried about corruption of the SD card.
You can record as it is like any other computers do, you just need to have a free space left on you sdcard todo so.
Also, there is a life expectancy for every storage device, it is called the read and write cycle, it may not affect your sdcard directly but it may in a longer run.
You can save your video files directly to the SD card - provided you have sufficient space on the card. "Sufficient space" will obviously depend upon what size card you have, and how big your video files are. I assume you can calculate this, and you haven't provided file or SD card sizes, so...
If you're worried about SD card corruption, you can always record to an external USB drive. To do so, you'll need to mount the external drive, and of course use that drive as the destination for your video files. If you need help mounting an external drive in Raspbian, there's a guide here you can follow.