You can make 5.6.1 work with on Mavericks with a workaround, as detailed here:
The issue with AirPort Utility v5.6.1 under OS X 10.9 Mavericks is
that a system file upon which AirPort Utility relies was updated in
10.9 and that update broke backwards compatibility with AirPort Utility v5.6.1. The file in question is Apple80211 in
Replacing this file with the older version allows AirPort Utility
v5.6.1 to be run under 10.9, but only via Terminal (i.e.,
double-clicking it will not launch it, it will throw an error).
However, there is a way to get around this issue by importing the older library into AirPort Utility v5.6.1 before running it. That is
what the new solution, downloadable, infra, does.