I charged up 3 x AA NiMh batteries. Got 4.26V. Then put a 50 mA load on it (like a Uno connected up). It dropped to 4.22V.
Extrapolated to 4 batteries that would be 5.67V under no load, and 5.63V under load. It's a bit high, but within absolute maximum ratings.
I think you will find that fully charged NiMh cells will only hold that higher cell voltage for a pretty short duration and then settle into a fairly flat discharge voltage for most of their duration until taking a pretty sharp decrease in cell voltage near the end of their capacity. Ni-cad cells have a similar 'flat' discharge curve, unlike lead acid or Li-po cells that have a pretty linear discharge voltage rate.http://www.atbatt.com/pics/fckeditor/image/lr44-discharge-chart.jpg