Yes BUT...
Question: Was the 5.2 measured? If so was it with or without a load.
BTW the Nano requires maybe 200 ma at the most. That means the power supply should be able to supply approx 2 X 200ma = 400ma MINIMUM for the powersupply. There is not MAXIMUM for the power. If you adapter was able to supply 100amps it would not matter, as long as the power could supply the 400 ma.
In the above I was very generous with the stated currents. In addition the 2x factor is a good design for lower power devices. If the adapter was only able to supply 200ma and the circuit draws 200 ma, it would be a marginal design. i.e. no headroom for safety.