An old newspaper puzzle with a cruel property: eight of the nine lines go down easily, and the ninth is always, always stuck. The reason is a conservation law for drawings — Euler's formula — and once you've counted with it, you also learn where the puzzle secretly IS solvable: on a doughnut.
Forget wires for a second and think about fences. Every closed loop you draw fences the yard into a room, and the sprawl outside the whole drawing is one more room. Add a wire that closes a loop and you gain exactly one room; add a wire that reaches somewhere new and you gain none. That trade is the only bookkeeping in this puzzle.
Now the catch. A room here can never have three walls, because a three-walled room would need a wire from a house to a house or a utility to a utility, and no such wire exists. Every room needs at least four. Nine wires, split two rooms apiece, supply eighteen walls. Five rooms at four walls each demand twenty. Twenty is more than eighteen, so the drawing you were asked for cannot exist — and the eight-wire version is already so tight that it uses every single wall it has.