I finally understand the question! Selenium Grid isn't the solution. But it does show that a job started by Jenkins can communicate with multiple servers.
I don't think
you should have 5 different jobs for your scenario. I would consider using a shell script for the deployments. (And have Jenkins kick off the shell script in one job.) This lets you have more control and do the deployments through ssh/scp commands.
Remember that you can have multiple build steps in Jenkins. The shell script that does the deployments can be one step. Running the tests can be another.