You can blow out the system using compressed air but you would need to take precautions or you will end up with silicone all over the floor. I use Speed-Bleeders on my jeep and when I bought them I also bought the kit. The kit consists of a vinyl bag that has a plastic hose leading into it. The other end of the hose is the right size to form a fairly tight fit over the nipple on the bleeder. Any expelled fuid goes straight into the bag.
Now you don't want to buy 4 kits but what you could do, and I have not tried this, is to buy clear plastic tubing at your local auto supply house, cut 4 sections, slip each over the nipple and run the other end into a can of some sort. I would also twist a piece of wire around the tube and nipple just so the air pressure doesn't blow it off.
Now you could crack open each bleeder and gently apply air pressure, perhaps through the vent in the cap?
OR, it might be easier to install a set of Speed-Bleeders, connect the drain tubes, and just keeping pumping and refilling until only the new stuff is coming out. If I remember correctly, the DOT5 is purple in color to differentiate it so once all the purple is expelled you should be good to go, or stop, as the case may be. �:)
Larry