Can I wait here in the US with an expired I-94?

I l might miss something, but five month out of status is way too long. Your application for change of status will not be approved if the course of study starts beyond the 30 days period.

Once you timely apply for a COS, you can legally remain in the US for 180 days while the application is pending or until a decision, whichever comes first.

Generally, an application for a change of status will not allow you to stay in the U.S. after your I-94 expires unless the start date begins immediately after the I-94 expires. Any gap will cause you to fall out of status and require you to leave the U.S. to apply for a new visa. Another possible issue is the denial of your I-539. USCIS does not like to change B-2's to F-1's unless the consulate noted such an intention on the B visa. If you have such a notation on your visa, you can request an extension of stay in the visitor status while waiting for school to start. I strongly suggest that you consult with an experienced immigration attorney. Good luck!