I passed the task using the split() method, but the first solution I had also delivered the same output, but failed the test (code below):
public static void main(String[] args) {
        System.out.println(getPartOfString("Amigo and Diego are best friends!"));
    }

    public static String getPartOfString(String string) throws StringTooShortException {
       try {
           int start = string.indexOf(" ") + 1;
           int secondSpace = string.indexOf(" ", start + 1);
           int thirdSpace = string.indexOf(" ", secondSpace + 1);
           int fourthSpace = string.indexOf(" ", thirdSpace + 1);
           int fifthSpace = string.indexOf(" ", fourthSpace + 1);
           return string.substring(start, fifthSpace);
       }catch (RuntimeException re){
           throw new StringTooShortException();
       }

    }

    public static class StringTooShortException extends RuntimeException {
    }