The default 5% superfat is a guideline established by tradition and time. There has been no particular magic or science used to determine this number. As Carolyn points out, it is entirely possible to make a reliably safe, mild soap with the superfat quite a bit lower, even without all the analytical testing that FordP is suggesting.
And also consider that the online calcs assume the NaOH purity is 100%, when we know it's really lower than that. The difference between 100% and the actual NaOH purity adds another few percent of "hidden" superfat to the soap, so that apparent 5% might actually be more like 7% to 10%.
My personal
soap calculator corrects for the NaOH purity, so my normal 3% superfat is a lot closer to a true 3% superfat than if I used an online calc. I have zero concerns about my soap being lye heavy. Even a superfat of zero to -1% or -2% will probably be fine for most people most of the time if using an online calc -- that will actually result in a neutral to slightly positive superfat. With my calc, I'd run the risk of making slightly lye heavy soap with those settings, based on personal experience, but I wouldn't be too worried -- soap a slight negative superfat will be fine after curing.
And most modern-day commercial soap is made with close to a zero superfat, but the commercial manufacturers do test the soap and handcrafted soap makers generally don't.
That said, the OP may have no recourse other than complying with the assessor's expectation that a 5% superfat is the right number to use. Sometimes that's just the way the world works.
How do you calculate superfatting by hand in your recipes?
Decide on the weights of the fats in your recipe. Use grams as the unit of weight.
NaOH for a fat, g = (NaOH saponification value for the fat) X (fat weight, grams)
Do this for each fat in your recipe.
Add up the individual NaOH weights you calculate. This is your total NaOH weight for the recipe at zero superfat.
Decide on your lye discount (aka superfat) in percent, then --
Total NaOH at a given superfat, g = (Total NaOH at zero superfat) X (100 - Superfat %) / 100
But use an online calc to do all these calculations. It's much easier and reduces the chance of error. I recommend
http://Soapee.com