Connecting Switch to a Rooter

Hi there,

I hope someone can help me with my question.

I currently have wireless internet, not fully though. Its a dish that's put up outside the house to catch the signals and then its connected via LAN (CAT5) cable to a Rooter inside the building. The CAT5 cable that comes from outside obviously goes into the WAN port on the Rooter and then the Rooter splits it into 4. Its then possible to plug in a total of 4 computers into the Rooter giving them all internet access.

I have 5 computers in the building though...

What I want to know is, will it work if I get a Switch and then plug in a cable into one of the 4 ports on the Rooter and then plug the other end into the Switch, and if I then plug computers into the switch will they be able to have internet access via this method, will it work??

Also no a wireless card for one of the computers is not a option

any info on this will be much appreciated