Can I connect one mac mini to another mac mini using a ethernet cable?

I have one Mac Mini that is currently connected to my network via wifi and would like to add a second mac mini to run some older programs. However, I would like to use the same monitor, wireless keyboard and mouse. Can I connect the add-on Mac Mini to the established Mac Mini using a Cat 5e ethernet cable? I think once I get it on the network I should just be able to access it once I turn on Sharing. I would set it up on the network by itself, but it's not recognizing my Apple keyboard, so I can't type in the wireless password to the network I need to get it on.