Connecting STM32F407VET06 to W5500 Ethernet
The first thing to do is verify that each pin is functioning. Get into the code and test each pin and make sure the logic levels  are correct and that you are actually talking to the pin that you intended to.
Get a logic analyzer (usb logic analyzers are cheap) and hook it up to the w5500 make sure the messages that you send have the correct clock and logic levels (verify this in the datasheet)
If that is correct then try and read back a register over SPI (set the IP register and read it back). Then you should be good to go.