Yes your Play 5 can connect to your home WiFi just as any Sonos product. When you open the app and go to the room with your Play 5 and click on it does WiFi show enabled? If not click the link below to re-enable WiFi.

https://support.sonos.com/en-us/article/disable-or-enable-wi-fi-on-your-sonos-products

If WiFi is enabled but you can only connect the Play 5 via Ethernet then I suggest you run a diagnostic and then call Sonos Tech support. You may have a faulty network card.

Yes it says WiFi enabled but still does not connect to it, only Ethernet works 

Have you recently changed WiFi? 

 When you’re trying to connect to WiFi is the Ethernet cable unplugged?  Not sure this is necessary.  Just asking.

 Was the 5 ever connected to any WiFi?  Does it need to be reset to connect to a new WiFi?

 I know…I know… More questions than answers.

If you are connecting on 2.4Ghz, confirm your router has 802.11b and/or 802.11g enabled.

If you are connecting on 5Ghz, confirm your Play:5 is Gen 2 and you have 802.11a enabled. If your Play:5 is not Gen 2, you'll have to connect it to 2.4Ghz.

Either case, confirm you have WPA2 (or less preferably WPA) enabled on your router. The Play:5 doesn't work with WPA3.

https://support.sonos.com/en-ca/article/supported-wifi-modes-and-security-standards-for-sonos-products