Rewrite cubic root (27x-81) - 5 to make it easier to graph using the translation.

Cubic root of (27x - 81) = cubic root of [27 (x-3) ] = 3 [cubic root of (x-3) ] - 5.

Then you can obtain this graph by shifting the graph [3 cubic root of x] three units to the right (which is what x - 3 does) and 5 units down (which is what subtracting 5 does).