555 high amperage charge pump inductorless voltage doubler
Get an inductor and do this right.  Charge pumps are inherently inefficient, and limited to relatively low currents.  This is in part due to the low efficiency, and in part due to the large capacitors that would be needed to pump high current.  Stepping 12 V to 20 V at 5 A out (100 W) is waaaaaayyyyyy beyond practical charge pump range.  Fahgeddaboudit!

The obvious answer is a boost converter, which, of course, will contain a inductor.  You have given no justification for avoiding inductors, so this is a viable answer.  There are boost converter ICs out there.  At this power level, you will need one that manages a external switch.

At 80% efficiency, for example, the average draw from the 12 V supply will be 10.4 A.  I would look into multi-phase architectures to split up that current.  At this power, you will probably have to design significant parts of the booster yourself.  There may not be any suitable off the shelf chips.  I'd probably look into a microcontroller driving three PWM outputs 120&deg; out of phase.

At 100 W, you have to wake up and do some real design, not just slap parts together according to a circuit you found in some questionable corner of the internet.  This is certainly no place for silly religious convictions, like that inductors are somehow evil.