Unlike with the PlayStation 4, in order to back up your PS5 save files, you will need to have PlayStation Plus membership, because the system currently only supports cloud backups.
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This means that you will not be able to simply copy your save files to a USB drive and have them on a safe place.
Instead, if you want to make sure that your progress will not be lost if something happens to the console, you'll need to pay for PS Plus membership and use the Cloud Storage feature.
PS Plus membership is priced at $9.99 monthly or $59.99 for a full year. Its main use is for online multiplayer because you can not play online games without it, but the service also offers monthly free games for the members.
People who are mostly interested in single-player games weren't the target audience of this service, but that might change if Sony permanently locks back up function behind it.
It's worth mentioning that PlayStation 5 has two separate Saved Data folders for your PS5 games and backwards compatible PS4 games.
Unlike next-gen games (PS5), you actually can export PS4 save files to an external USB stick or USB drive.
This gives PlayStation 5 owners a grain of hope that the same functionality will eventually be added for the next-gen games as well, as PS5 offers you the ability to export your PS4 save files.
Locking the ability to back up your save files behind a paywall is something Nintendo is already doing with the Switch console, where backing up requires Switch Online membership, which cost $3.99 USD monthly or $19.99 USD if you pay a year upfront.
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Besides the obvious issue of taking players' ability to back up files themselves, there are also other problems, like games not having cloud saving compatibility, when players are having issues with the internet, or when you want to play your saved game someone's other console.