do not worry

1) submit your application as soon as possible.
2) attach a letter to explain the gap(5 days?). and state that you are innocent, this is not your fault but the international office delay.
3) for some case, the INS could consider your explaination, and grant you H1b without reentering US.
4) if they ask you to reenter us to clear your gap, then you have to do so. but it is also not a worry.
5) just do your best to take the chance, and God bless.