This explaination may be a bit muddy, but:
Toomanyuserprofiles So what exactly is socks5?
In simple words, SOCKS is just a protocol that allows proxying, there are a small bunch of protocols that do proxying and SOCKS5 is one of them.
SOCKS proxies are done on the application layer, so they are usually options specified by individual applications rather entire operating systems or networks. The Tor connection on Tor Browser is done by a Proxy since it is just for the application. For situations like an entire OS or network then a VPN protocol (IPsec, WireGuard, OpenVPN etc) would fill that place instead.
Toomanyuserprofiles And more importantly, when and why should we be choosing it as an option?
It would be used if you want to manually select an app to choose a different connection than your current one. See the next part for a better descriptive answer.
While SOCKS proxies often get posted around as a method of hiding your IP address or circumvention they aren't really that useful for either. Proxies like these are used more for authentication or access or for single applications, for example using a SOCKS proxy to SSH into a server that isn't possible to access without. You may be on a network where you aren't able to access something externally without a proxy. VPNs also do these, but proxies serve as an alternative. Some apps like Tor have a SOCKS feature for networks that need to use one to access the Internet. Another example is the penetration testing application Burp Suite uses a proxy you set up into a web browser to intercept your web requests between you and the target. SOCKS is more of a networking thing than a privacy/security one.
If you have a VPN the use of a SOCKS proxy is irrelevant and would just be an extra layer. A flaw with the SOCKS protocol is that it is not encrypted, so if you access an unencrypted resource like HTTP through a SOCKS proxy then it goes back to you unencrypted as well. The SOCKS proxy would need an extra layer of privacy such as connection to a VPN or Tor on their end or yours to mitigate. Someone monitoring the network would just see this unencrypted information but have a source IP of the SOCKS proxy instead. While it does hide your IP address, it wouldn't make much sense since it would apply to just that app. VPN protocols with encryption will encrypt the traffic when they go back to you, meaning they would only see the connection of the VPN, not the content itself.
Toomanyuserprofiles Similar questions- invizivle pro has an option to use Tue app as a VPN or a proxy. How does the proxy work though?
I don't use it, but I imagine it likely works by the app creating a Proxy server on your device with it's own port. With that then you can specify individual apps to use that proxy, which would then go through Tor via the connection InviZible Pro sets up. This would be immune to the privacy issues of SOCKS I mentioned prior since it's using Tor as an additional layer (and if you are using a VPN with it, it's irrelevant), but the use case for this is you can specify single apps to go through Tor by making these apps choose the Proxy that InviZible sets up.