GI 3.9.1 does not officially support Firefox 5. [*Edit* _This applies to Firefox 5+ (5,6,7, and probably 8+_)] However...
As far as we know GI 3.9.1 does run on Firefox 5. However there's been report of issue with GI Builder that turn out to be related to the old same origin policy issue. To run GI Builder on Firefox 5, you must make sure that the security.fileuri.strict_origin_policy flag is set to false in the about:config tab.
Only change this flag on your GI Firefox profile and not your web-browsing default Firefox profile. For instruction on how to create your custom GI Builder profile, See http://support.mozilla.com/en-US/kb/Profiles
You will no longer be able to run webservice call directly from inside Builder due to this change in Firefox 5.
See the security note https://developer.mozilla.org/En/Using_XMLHttpRequest#Security
|Firefox 5 note|
Versions of Firefox prior to Firefox 5 could use netscape.security.PrivilegeManager.enablePrivilege("UniversalBrowserRead"); to request cross-site access. This is no longer supported, even though it produces no warning and permission dialog is still presented.
The recommended way to enable cross-site scripting is to use the Access-Control-Allow-Origin HTTP header in the response to the XMLHttpRequest.