Welcome to the Wefugees Community and thank you for reaching out to us.
I am unfortunately not very experienced in this topic. But if I am not mistaken, the re-entry ban might be even valid for the whole Schengen area. This would mean that other EU countries most probably would not issue a visa in the first place. As far as I know, you also would need to apply for an exceptional permit to enter Germany during the 5 years of your entry-ban.
Another issue is the so-called Dublin regulation which roughly states, that in general the visa issuing country is also responsible for your asylum case. As you can see, your plan to re-apply for asylum in Germany after having received supporting benefits in the context of a voluntary return will be very very difficult. I am sorry that I can not give you a more positive answer.
Nevertheless, I will also link our expert @alla_fka here. Maybe she can give some further information and advice.
All the best,