Downgrade to iOS 7 on iPhone 5s = Impossible (except dual-boot).
If you are attempting a downgrade, you are likely interested in either or Exploitation (downgrading without blobs) . iphone 5s ios 7 downgrade
The iPhone 5s, released in 2013, was a significant upgrade to the iPhone lineup, featuring a powerful A7 chip, improved camera, and fingerprint recognition technology, Touch ID. Alongside its release, Apple launched iOS 7, a major overhaul of the iPhone's operating system, introducing a new design language and several innovative features. Downgrade to iOS 7 on iPhone 5s =
If you did not save digital signatures (blobs) while Apple was still signing iOS 7, you are limited to a tethered downgrade. Method 1: The "Tethered" Downgrade (No Blobs Needed) released in 2013