How close does your GPS Series 5 watch need to be to your iPhone to work?

Your Series 5 Watch GPS must be in either Bluetooth range of the paired iPhone or in Wi-Fi range. You can find typical Bluetooth ranges here:

https://blog.nordicsemi.com/getconnected/things-you-should-know-about-bluetooth-range

& typical WI-FI range here:

https://www.lifewire.com/range-of-typical-wifi-network-816564

but your milage may vary.

If you are away from a wi-fi network known to your phone, I would guess the Bluetooth distance 10 m/ 30 f.

ASC - Late 2012 Mac mini, macOS 10.14.6; Watch, series 5 GPS/cellular, watchOS 6.2.8; iPad Air 2, ipadOS 13.6.1; iPhone 8+, iOS 13.6.1; TV 4th Gen, tvOS 13.4.8;  HomePods, audioOS 13.4.8 and Airport Express w/ Airplay 2

De nada.