Did you supply 5V to the module? I did not have experience with it, but W5200 used in this module should be powered by 3.3V. It is declared that chip’s inputs are 5V tolerant though, but I do not recommend feeding it with 5V input signals as it creates excessive consumption current.
If you are looking for quick way doing it, then just connect RSTn to 3.3V supply rail directly or through 1k resistor if possible. However you must keep in mind that before reset goes high, it is highly recommended to have it low for specific amount of time stated in the datasheet.
If you are looking for proper solution for the reset input, then there’re a number of circuits and manuals explaining how to generate proper digital reset signal, ranging from simple having button, resistor and cap like this one up to several specific chips designed for proper timing and signal cleanness like this one.
Reset: Low activity
This pin is to initialize WIZ550io.
Hold at least 500us after asserted to LOW and wait for at least 150ms after it is changed to HIGH until WIY550io configured itself.
This pin is asserted to low after power on.
When RSTn is activated, WIZ550io does auto configuration with embedded MAC and default IP address.
After configuration gets completed, WIZ550io raises this pin to HIGH in order to inform about the completion of WIZ550io’s configuration.
Host processor can only control WIZ55oio when RDY pin is HIGH.