The arduino Ethernet library only supports the W5100 Ethernet controller found on the Ethernet Shield, and not the W5500 on your Ethernet Shield 2. If you want to continue using the arduino.cc IDE, which is under much more active development and has stronger community support, you can copy the Ethernet2 library from the arduino.org IDE installation to your sketchbook/libraries folder or use one of these alternative Ethernet libraries which support the W5500: