On MANY smaller lenses, f/5.6 is the "lowest numerical value" that the lens has when the lens is zoomed out a bit. For example, on an 18-55 f/3.5~5.6 zoom lens, the lowest f/number is f/3.5 at 18mm, but the maximum aperture size changes as the lens is zoomed, and the f/number's value hits f/5.6 somewhere in the zoom range. So....again, it's quite possible that the reason you can not get the f/number value LOWER THAN 5.6 is that...the lens has been zoomed out a bit.
Another example, in Av mode, you can use the command dial on the camera to set the lens to f/3.5 with the zoom set at its shortest length, like say 18mm...but when you manually zoom the lens to a longer length, like say 28mm, it might drop to oh, say f/4.5 or f/4.8, and then to f/5, then to f/5.6 at the longest end...which is the way a variable maximum aperture zoom lens of any brand will behave.