Need Mac .sh to run command line app in seperate terminal

Hello, currently we are executing a .sh from terminal.

The current .sh looks like this:

#!/usr/bin/env bash

/Users/user/my.app/Contents/MacOS/my &

--

Now, we also need to run a third line in the .sh - It's a command line application that I need to run when I execute the above .sh however the new line that runs this command line application, I need to make sure runs in a separate terminal window then the above application AND it will need a 5 second head start on the current applications inside of the above .sh

What would my new .sh file look like?

Thanks.