If you follow the "help" tab in your Account Manager, you will be taken to the "Bravenet Help Center". On the right, under "Helpful Resources..." are several links that might help. The one on "PHP Program Compatibility" will give you a list of PHP software that has been tested and verified. But they still don't give a version number.
If you follow the "Knowlege Base" link, again under "Helpful Resources...", and do a search on PHP, you will get the following:
5. What version of PHP do you support? We are running the latest version of PHP.
If you need more information than that, contact Bravenet directly, through one of their trouble tickets.