10 pounds of ice won't cool 5 gallons of boiling wort. The ice will melt and the water bath will warm.
I have a friend who buys several big bags of ice (about 4?) but I don't know how many pounds that is exactly. It won't fit in a sink, but it puts the ice in a huge cooler (maybe 60 quarts?) and then drops the boil kettle into that. He stirs both the ice bath and the wort and it is pretty cool in about 20 minutes, at least cool enough that he can pitch shortly thereafter.
He puts the boil kettle in that cooler, then keeps the kettle in there and siphons the beer out of it, after draining off some of the warm water. I wouldn't have thought it would work so well- but I've seen it with my own eyes and know it works great for him. But it's probably more like 40 pounds of ice, and not 10.