Welcome back to the Wefugees Community and thank you for reaching out to us again.
I actually never heard of such a law stating that people are granted automatically a residence permit after staying in Germany for more than five years. But I will also link our dear expert @alla_fka here. Maybe she has some alternative information.
In general, there is the option to file an action for failure to act ("Untätigkeitsklage") against the BAMF. However, it is not unusual that the procedures at the BAMF take several months minimum. I am not sure though if waiting for the decision for about one year (since only one year ago the responsibility for the asylum application was transferred to the German government) already "qualifies" for such a step. I would recommend you to discuss this with your lawyer or in a legal counselling office.
One positive aspect: If your parents are granted the refugee status, their wating periods of the pending asylum procedure may be "counted" as well in case they are applying for a permanent residence permit (Niederlassungserlaubnis) later on.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,