I wish to ship some luggage from Frankfurt airport to the hotel. I checked DE Bahn, it takes five working days. Are there other companies that can ship faster?
I checked the webpage of DE Bahn because I found it odd that they would pick up luggage at the airport and I couldn't find the service you describe.
They offer an airport service where they ship your luggage to the airport and store it there for you to pick it up, and they have a cooperation with the German courier company "Hermes" which is described here.
You are probably referring to the latter. But I am pretty sure they don't pick it up at the airport on their own because the service is designed to collect your luggage at home or your company and deliver it to the airport or your destination before you actually arrive there.
The former seems to be a cooperation with the Luggage service of Frankfurt Airport where they store luggage for you up to 3 months and if you want to send it back to you.
Check the website of the luggage service here.