Unfortunately Apple dropped support for the iPhone 5S with the release of iOS 13. The current iOS version for iPhone 5S is iOS 12.5. 1 (released on January 11, 2021).

How can I update my iPhone 5 to iOS 13?

Downloading and installing iOS 13 on your iPhone or iPod Touch

1. On your iPhone or iPod Touch, head to Settings > General > Software Update.
2. This will push your device to check for available updates, and you’ll see a message that iOS 13 is available.

Can iPhone 5S get iOS 13?

An iPhone 5S won’t upgrade beyond iOS 12.5. 8. To upgrade it to iOS 13, you’ll need an iPhone 7 or later. iPhone 6S / 6S Plus can also be updated to iOS 14.