Note both the Sonos (mobile) controller and the speakers need to be on the same network and so I recommend you put all onto your Google mesh, as that’s likely where you are connecting your mobile device to (I presume?) ..aswell as the majority of your Sonos devices.
You really/ideally need to start by removing/forgetting the initial (ISP provided) routers WiFi network from your mobile device and switching off the WiFi adapters on your router too, which are not needed now that you are using the Google WiFi instead. You may need to check your router user-manual to perhaps change that setting as the settings are often different for each router brand, or model. I hope you, or a friend/family member, or colleague, can perhaps sort it.🤞
You need to also see if you have both WiFi networks (Google and Router) stored in your Sonos App network settings. If you do then remove just the Routers WiFi SSID only - here’s a link to explain how to do that…
https://support.sonos.com/en-us/article/remove-a-wifi-network-from-your-sonos-system
If your Sonos Five is part of your existing Sonos Household, then on reboot it should connect back to the Google WiFi when you have completed the steps mentioned above. If however it’s become part of a separate Sonos Household then you will need to factory reset it (having completed the steps mentioned) and then add it back to your original Sonos setup as a new device.
The instructions to factory reset your device, if needed, are shown here in this link:
https://support.sonos.com/en-us/article/reset-your-sonos-product
I’m sorry I cannot make/explain things any easier, but if you’re struggling to resolve the issue then hopefully you can find someone to assist you, or perhaps call Sonos Support and see if they can assist you. Here is a link to call them…
https://support.sonos.com/s/contact