Can I leave my iPhone home and still have it connected with the watch 5 miles out?

Hi

Your watch may be able to offer certain features when the paired iPhone is not taken along by connecting to the gym's Wi-Fi network.

The full range of features - including calling and texting - is available when Apple Watch and iPhone are connected. Whenever possible, the devices will connect via Bluetooth (range is normally around 33 feet / 10 meters, but this may vary in practice due to wireless interference).

Whenever your watch can't connect to the iPhone via Bluetooth, it will attempt, as a fallback, to connect to a known, compatible Wi-Fi network.

Your watch can connect to a Wi-Fi network if the network is 802.11b/g/n 2.4GHz and the paired iPhone, while connected to the watch via Bluetooth, has connected to that network before. Apple Watch will not connect to 5GHz Wi-Fi or to public / workplace networks that require logins, subscriptions or profiles.

When instead connected to Wi-Fi, the watch also still offers a number of features, including receiving and sending messages via iMessage. If your carrier offers Wi-Fi Calling and it is supported on your plan and enabled on your iPhone, you can also use Apple Watch to make calls and (subject to carrier support) send and receive texts.

If your watch is unable to connect either via Bluetooth or Wi-Fi, it again still offers some - although fewer - features.

Features that remain available in each case are detailed here:

How to use your Apple Watch without your iPhone nearby - Apple Support

For the best performance from your iPhone and Apple Watch, including the most power-efficient communication between them, Apple recommends keeping both Bluetooth and Wi-Fi permanently enabled on your iPhone.

More information:

About Bluetooth and Wi-Fi on Apple Watch - Apple Support

You can try connecting both to the gym facilities WiFi and make that a trusted hotspot but you cannot connect to your iPhone from that distance.