The Sonos Play:5 doesn’t have built-in voice control capabilities like the Sonos Beam, so it won’t show up in the menu for adding Google Assistant in the Sonos app.
It can be controlled using a separate voice controlled speaker though, which is want you want to do.
You can either add Google Assistant to your Beam, after which your Play:5 should show up in the Google Home app automatically.
Or, open the Google Home app, select “+” at the top left, then “Set up a device”, followed by “Works with Google”. Tap the search icon at the top right and search for “Sonos”.
Select “Sonos”, after which you will have to log in to your Sonos account and grant Google access to your Sonos devices.
All your Sonos devices, including your Play:5, should now be visible in the Google Home app.
To make things easier, set your Play:5 as the default speaker for your Nest Mini: https://support.google.com/googlenest/answer/7532812?co=GENIE.Platform%3DAndroid&hl=en