I don't recall if the 5s can be "re-paired" to the logic board. However, there are a series of machines that Apple has that can at least reset a home button/Touch ID to the logic board for some models. It's mentioned in this article where Apple gave access to the repair development lab in Sunnyvale, California.
https://www.reuters.com/article/us-apple-repair-exclusive/exclusive-apple-makes- iphone-screen-fixes-easier-as-states-mul…
But the Horizon Machine is needed to remedy the trickiest mishaps, such as when the fingerprint sensor attached to the back of the glass gets damaged when a phone is dropped.
For security, only Apple’s fix-it machine can tell the iPhone’s processor, its silicon brain, to recognize a replacement sensor. Without it, the iPhone won’t unlock with the touch of a finger. Banking apps that require a fingerprint won’t work either, including the Apple Pay digital wallet.
That's why I say perhaps you can ask if Apple might be able to do this. Again, I'm not sure if a 5s is something that they can do or if it was still from the era where Apple only issued complete replacements for any repair.