I assume you are using four (4) cell Nicd battery. It has a nominal voltage of 4.8. However, a freshly charged battery can test at well over 5 volts. I see you are using a load on your tester. Good, always use a loaded tested. You can get false reading otherwise.

When used, Nicd batteries drop rapidly to a ~4.8 volt loaded test. They "hang" in this 4.8V range for a long time, then they drop rapidly to zero. Because of this, I agree with what your manual said, don't fly if they test below 4.8 volts.

If you have a cycler, you can kinda double check this. Fly until you get a volt test reading under 4.8v. Drain the battery on a cycler that can measure capacity and see how much of the pack you have left.

When I do this with my packs, I end up having about 1/3 of the rated charge left in the pack. Technically I could fly until I have 0% of the charge left, but I feel only draining to about 33% gives me a nice safety buffer.