This happens when the wrong passcode was entered too many times. You'll need a version of iTunes that is compatible with the iOS on a iPhone 5S. The latest generation of iPhone is the 15, so this is like 10 generations behind and is from 2013. You'll need a Mac from the Mountain Lion, Mavericks or Yosemite (maybe El Capitan) era with the correct version.
Once you do have the right version of iTunes, once connected, your only option is to reset the device thus losing everything on there. The normal course of action after that is to restore a backup to the device. If you don't have a device, then you've lost everything.
Later versions of iPhone supported backing up to the cloud, but not sure the 5S supported that.
So if this phone wasn't backed up, then you'll essentially have to set it up as a new device.