Since - according to the screen shot - you are not using VLANs, you'll have to add another vSwitch with separate uplink(s) to physical switch port(s) which are configured for the Internet subnet.
Hi Oscar ,
We welcome you the VMware support community.
Looking at the screen shot it is clear that your vmnic4 or vmnic5 are disabled. This might be because it is disabled in BIOS or there are hardware issues .
The vmnics are physical network ports available on your ESXi hosts which are used to communicate outside your vsphere environment.
Please go to the properties on the vSwitch and try adding other network adapters which are functional.
You can check the network adapters available by clicking on the 'network adapter' on the left hand side panel