For that simple a text:
this (is) an (example) string given (for) text between (parenthesis).
It's relatively simple - you just need to keep processing, starting each time from the index of the closing parenthesis you just used.
So just change your code to add a loop, and keep looping until IndexOf returns a negative number when looking for a '(', and update start1 each time your finish colouring a section.
But...you might want to think a little more carefully about what you are doing: nested parentheses will cause you real problems!
this (is) an (example string given (for) text) between (parenthesis).
Would need you to colour the whole of
"example string given (for) text"
not stop after the first ')'.