Why can’t I pair my Apple Watch series 5 to my iPhone 6s?

Are you sure you have an iPhone 6s, and not an iPhone 6 or iPhone 6 Plus?

Check iPhone -> Settings -> General -> About

The current shipping Apple Watch Series 3 and 5 require an iPhone 6s, SE, 7 or newer running iOS 13. The iPhone 6 and older cannot upgrade to iOS 13

Apple Holiday Return Policy (Purchase between: 15-Nov-2019 thru 25-Dec-2019, Return by 8-Jan-2020)

All purchases made before November 15, 2019 and after December 25, 2019, are subject to the Standard 14-day Return Policy. 

https://www.apple.com/shop/help/returns_refund

Probably because it's not a 6s.

What is the model number in Settings>General>About?

The watch requires an iPhone running iOS 13.