The ability to add extra PS5 SSD storage is coming in a future system update, but Sony recommends you hold off on buying any early.
Sony just posted a big FAQ about PS5 on the PlayStation Blog, covering a wide range of topics about the console. One of the most important points for early adopters is how users will be able to install M.2 SSD drives to expand their PS5's built-in storage, and when they'll actually be able to do it.
M.2 SSD drives are a computer component that offer solid-state storage at even higher speeds than earlier SSD form factors, thanks in part to the way they directly connect to a PC's motherboard. We've known you'll be able to plug one into your PS5 for a while, but Sony confirmed in the FAQ post that the functionality will be added to the console in a post-launch software update. It didn't say how long we should expect to wait for M.2 SSD storage to be enabled.
On top of that, Sony confirmed that only M.2 SSDs which meet a "minimum performance level" will be compatible with PS5. Since it isn't ready to reveal the specific specs your additional storage will need at the moment, Sony recommends you don't try to pick one up early (which is a bummer, since the Black Friday gaming deals are already starting to get good).
If you already have an external hard drive for your PS4, you'll be able to keep using it to store and play PS4 games on PS5. However, Sony is currently only 'exploring' the possibility of letting PS5 games be stored this way - and in any case, they'd need to be transferred back to the internal SSD before you could play them.