Depends how good your battery is. Is it a new pack? What sort of condition is it in? Packs that have a lower C rating will have their voltage pulled down further than higher C rating packs. Packs that have been consistently over discharged or have puffed from being left fully charged will also sag a lot more under load than packs in good health.
BTW. What are you flying where you can get a cruising current of only 5A? Even my F450 is up around 20 or so!
Hi, it does sound like internal resistance in the battery being too high.
Try to see if your battery charger can measure that. If not and if you know what your are doing with electric circuits, you can also connect eg. an automotive light bulb as a test load, and see by how much the voltage drops when you do that. OK 4S is a little much for the bulb but it is only for a few seconds. You also need to know the current through the bulb (a separate measurement). Divide the voltage drop by the current and you get the internal resistance. It should only be like 5 to 25 milliohms for a big battery like that.
I had lots of lipos recently go high on internal resistance without any reason - wonder if they all got worse in quality the last 1 or 2 years?
Unfortunately, LiPo batteries are pretty fragile, considering the beating they can cop in our applications. It doesn't take much (a few really low discharges for eg) for them to get a bit sad. Leaving them fully charged and then having them get hot seems to be the worst for that though. I always put my packs on 'storage charge' after I've finished with them for the day. Since I started doing this, I haven't had a single pack fail prematurely.