The PlayStation 5 comes packing an 825GB SSD, where you'll be able to store all your PS4 and PS5 games.
However, with lots of big titles being the size they are these days, that's going to fill up pretty quickly.
During his recent presentation, Mark Cerny confirmed that PS5 will be compatible with regular external hard drives, like the ones that currently work with PS4. The advantage of this is that you'll be able to just use the external HDD you already have, or purchase a relatively inexpensive one.
The downside to using one of these is that you won't gain the benefit of the SSD's impressive load speeds.
However, that's not your only option. You'll also be able to make use of NVMe drives, which are essentially external SSDs. This is similar to what Microsoft is doing for Xbox Series X. The problem is -- without going technobabble mad -- there are no NVMe drives on the market that match up to PS5's internal SSD.
In other words, to get the best use out of this method of extra storage, you'll need to wait until NVMe drives for PCs catch up to PS5's capabilities. The downside to this is that it could be quite an expensive investment.
Still, it sounds like you'll have plenty of options when it comes to extra storage space.