Consumer electronics like this which are sold where the end user installs often have some sort of method to tolerate little mishaps because returns are very expensive. In this case, its a LED light fixture and those can be designed to tolerate reverse hookup. And sometimes even work fine hooked up either way. More tolerant adds cost to the design.We have seen plenty of equipment destroyed by reverse polarity despite the correct size fuse being used.
A very simple method sometime used in designs is to put a diode across the input power. If you hook up the DC power correctly, the diode is reverse biased and doesnt do anything. If you hook up the power backwards, the diode is forward biased and looks somewhat like a short. This is meant to work in conjunction with a fuse where when hooked up backwards, the input diode gets forward biased and "lots" of current flows and causes the fuse (easy to replace) to blow. The fuse needs to blow before the diode does - hence the current rating of the fuse.
We really dont know why the manufacture said to put a 1 amp fuse in that line and without looking at the schematic, wont know. Will the OP have any issue ignoring the 1 amp? Most likely the worst case is just burning out the device and then returning it for another. The manufacture is trying to avoid this but you probably have that option. Is there any safety risk by ignoring the manufactures fuse recommendation? All most for sure not since you have any case of wire short covered with the 5 amp fuse.
The OP is not getting bad advice here to blow off the 1 amp fuse. Im just pointing out (as a retired consumer electronics design engineer) one possible reason the 1 amp fuse is specified by the manufacture.