I agree with Attorney West. Please remember there is no grace period for H1B holders like F-1 students. Once you resign, you will be out of status.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. Consult with a qualified attorney before making any legal decisions. Gen Kimura, (832) 247-6932.
There is no formal grace period to be in the country after the H1B is terminated -- leave as soon as you can -- 5 days sounds like it should not pose future problems. Keep a record of what you are trying to accomplish during this time so you can explain your "overstay" if you need to down the road.
An attorney-client relationship is not formed by my responses to questions on Avvo. My responses are not intended to be legal advice and must not be relied upon as legal advice.