How do I unpair my watch if it isn’t working at all?

What do you mean by "not working at all" ? Perhaps the best test to check if there is any life left in it is trying the hard reset option first:

• Press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.

How to restart your Apple Watch - Apple Support

If that fails, the issue could be your battery or no charge. Check this guidance for that part:

If your Apple Watch won't charge or it won't turn on - Apple Support

Finally, here the unpair guidance too:

Unpair and erase your Apple Watch - Apple Support

In that case I would consider the battery & power replacement service:

iPhone Battery Replacement - Official Apple Support

It is still a fairly new model (S5 right?), so should still have many good years of life in it.