Router is trasparnet to communications. “It just conects the cables” Nothing more to do with your wiz550. Only your pc and wiz550 must be in the same network that means all of them must have 192.168.1.xx where xx is a different number for each device fo example your pc may be 192.168.1.250 and wiz550 is 192.168.1.2 then the command (from pc) ping 192.168.1.2 will have a regulary responce from the wiz550.
Routers have protocols to descover which is the ip for every device connected at their gate (jack) Supose this example
you cahnge your pc have 10.97.0.100 , the wiz550 have 10.97.0.101 ( don’t ask how , you will learn latter) the router 192.168.0.1 From your pc you can issue the command ping 10.97.0.101 and the wiz550 will responce Why ? the router when you plug the cable on it and the yellow/ green led blinks fired a protocol to descover the ip of the device plunged on it.
Now with the same ip to PC (10.97.0.100) and at the properties of lan driver set mask 255.255.255.0 and gateway 192.168.0.1 (router ip) and from firefox google.com --> you will see the google’s page Because of TCP protocol is routeable
Of course you can change the ip by code Think about it If you got one wiz550 more … or 2 of them They will have the same ip. you will face a conflict with these modules on your network. So you have to change the ip to all of them.
THAT MEANS THAT you have to write code to present a html page to the client (someting like 192.168.1.16:90/admin ) so the client who will buy your device, aparatus etc , to be able to change the ip (for static ip) of the best that all comerce device do to look for then DHCP on the network to ask for a free ip on the network, which will be applied to wiz550.
google , question like "ardiuno and w5500 program ip"
you will find tons of code
AND PLEASE BEFOR ALL READ wiz550 datasheet, w5500 datasheet, at wikipedia read what is DHCP, what is DNS