You can have 5x the voltage without changing the power consumption if you reduce the capacitance. If you keep the transistors at the same size, a computer working with 5x mode voltage will use 5x more power if operating at the same frequency. (But you can probably make it run faster...)
That said, except for very few embedded applications, computers today operate on a voltage that's much bigger than the silicon band gap. I'm not convinced it'd be a problem.
The silicon band gap is ~1.1V at room temperature. Mainstream modern processor core voltages are around 1.2V (maybe less for the very latest parts) and "ultra low voltage" processors operate as low as 0.7V.
That said, except for very few embedded applications, computers today operate on a voltage that's much bigger than the silicon band gap. I'm not convinced it'd be a problem.