Hello again @Hellothere,
For me it is somehow not clear yet which document you are currently holding (since your stay is not "illegal" in Germany). Unfortunately, I am also not familiar with the "five days valid travel document" you are referring to.
In case you want to apply for asylum, I would highly recommend you to contact a counselling office in Berlin to discuss your case and your chances. The so-called "Asylverfahrensberatung" (in Berlin, the AWO is providing this specialised service) might be one option. Once you decide to apply for asylum, you will be required to stay in the refugee reception centre. In the first months, you will be most probably not be able to obtain a work permit. Please see Handbook Germany for more details on this.
Whether you are in the asylum procedure or not, the registry office (Standesamt) is most likely asking for a valid passport for the marriage as well. I answered this question (which you raised in another thread before) here. A side note: Please also keep in mind that a sham or fake marriage is illegal in Germany and causes many problems. The authorities can be very alert and may suspect a marriage only be concluded to legalise a stay of a foreigner in Germany.
I hope these information are helpful and please don't hesitate to get back to us with any further questions.
All the best,
Meike