Preheat oven to 325. Boil water in kettle for water bath.
Melt 5-6 tablespoons of sugar in pan, then coat bottom and sides of flan pan.
In mixing bowl, mix together 3/4 C sugar and lime zest.
Add egg yolks one at a time; mix well between each addition.
Add whole egg and mix well. Add can of evaporated milk, blend in.
Pour into coated flan pan. Place in large baking pan and pour in hot water half-way up flan pan. Bake 1 hour, then continue another 30 to 40 minutes, checking every 15 to 20 minutes for firmness (shake flan pan to check firmness). If necessary, cover flan pan with foil halfway through baking to prevent burning. Remove from water bath and cool 30 minutes. Cover and refrigerate until completely cool (can be left overnight). Run a sharp knife around edge of flan and invert into serving dish.