With the exception of upside-down type cakes that have a layer of fruit in the bottom (those have to come out right away), I usually leave cakes (quick breads, etc.) in their pan until I can stand to hold my hand against the pan for a few seconds. Still very warm, but not oven hot. Often that's longer than the 10 minutes most recipes suggest.
Couple things to spot check. Even a non-stick pan should be sprayed/buttered and dusted with flour to help the cake release. Also, a little cheat I learned from a friend. Some cakes don't rise all the way to the top of their pan (maybe it was the recipe, maybe the cake, whatever), so when you invert them, they have an inch or more to drop before they hit the plate/platter. That could be disastrous for a warm cake. I stuff the empty gap between the cake and the top of the pan with three or four flattened balls of crumpled foil, invert onto a plate, and slowly jiggle the cake pan away from the cake. No dangerous drop for the cake.
And when all else fails, you can serve the cake pre-sliced on a beautiful tray with lots of fancy paper lace doilies, or in paper/foil cups, or cut it up and layer it in a glass bowl with lots of whipped cream and call it an apple trifle. No one will ever know