On a 100 amp service I would say you are right near the limit. Your Haas/RPC system is around 60 amps. A 5 HP compressor is around 25 amps @ 240V single phase. That gives you enough left over to run a couple of light bulbs.
There ain't no free lunch, your power problem is not going to go away. Let's look at the numbers:
(I'm not going to figure in power factor and efficiency here, we're just going to treat this as resistive loads, close enough for this calculation)
You have 24000 watts total power available. 1 HP = 746 watts, so we'll round that to 750 W/HP
Spindle
20 HP * 750 = 15000, 24000 - 15000 = 9000 W left
Compressor
5 HP * 750 = 3750, 9000 - 3750 = 5250 W left
That means you have enough power left to run a 3 HP (2250W) knee mill and still have enough reserve for a couple of light bulbs.
Now throw in the power that the RPC is using itself and your breaker trips.
Now your Haas is not running at full load all the time, so we can add back a little reserve, but not much.
I also have 100 amps of 240V single phase. I'm faced with the same problem but I approached it a bit differently, I looked at the power first and bought machines to match.
Haas TM-2p 7.5HP, running on single phase, 5625 W
CNC lathe, 10 HP spindle running on a 15HP RPC, 9000 W
3 HP knee mill, 2250 W
5 HP compressor, 3 phase, but running on a VFD fed by single phase, 3750W
So my total is about 22,000 watts max load. The only way I get away with this is that none of the machines run at full power all of the time. With all of the machines running my total power draw averages about 12,000 watts with peaks to around 20,000 watts. You have to have enough power available to handle the peaks or you are going to be tripping the main.
Bottom line is you can add a 5 hp compressor, but not another Haas.
EDIT: corrected the compressor power usage.