From what I see here it looks like you scanned the internal IP address of your router (also your default gateway). The services that you see running should only be accessible from inside your network on the default gateway IP address.
Port 23: Telnet - Command line access to administer your router.
Port 53 DNS (domain name service) - resolves hostnames to ip addresses.
Port 80 HTTP - a webserver running the graphical interface used to administer your Router.
Port 5000 UPNP (universal plug and play) - This is a network discovery protocol which allows devices to find and configure other network devices.
As far as which services are needed to browse the web technically none of them are needed. However some of these services are required for you to administer your device. If you can disable telnet I would recommend that be turned off unless you prefer to configure it via the command line. If you do prefer CLI administration I would look into seeing if your device supports SSH as it is more secure. DNS can also be turned off on your router I recommend using your ISP's DNS servers as they tend to be the fastest available option but this is always debatable. Regardless of this fact DNS is optional. UPNP is also optional but it should be turned off unless you require it.
As far as your public facing IP address goes I would scan the ports from and outside host or using a service like shields up. All ports can and should be closed if you are using your service primarily to browse the internet.