Apple Watch 5 fall detection

Yes (maybe)

Generally the Apple Watch needs to be able to make a phone call. If you do have a Cellular Apple Watch, then uses your iPhone if it can find your iPhone.

One special case would be, if your iPhone carrier supports WiFi calling, And you have enabled WiFi calling on your iPhone, And you have enabled WiFi calling on your Apple Watch, And your Apple Watch is connected to WiFi, then the Apple Watch can use WiFi calling to make an emergency services call. But this tends to be you home, and if you are home, chances are your iPhone is nearby.

The Series 5 Cellular model can make an emergency service call WITHOUT paying for a cellular contract. While you would have to pay more up front for the Apple Watch, you would not need to make the on-going monthly payment to your cellular carrier.

Series 5 Fall Detection and Emergency Services on Cellular Apple Watch Series 5 with no cellular contract

https://support.apple.com/HT206983

https://www.apple.com/watchos/feature-availability/#branded-international-emergency

https://support.apple.com/HT208944

The Series 5 GPS+Cellular can. NOT the older models, and NOT the GPS only models.