External storage from PS4 to PS5

Hi, I just bought a PS5, and I was wondering how the external storage works. I already had a 2TB external storage unit on my PS4, I tried hooking it into my PS5 and it works, but I'm not able to download PS5 games on it. I'm able to play all of my previously installed PS4 games. Do I have to format it? Will I need to delete everything by formatting it again for my PS5?