Your touchscreen controller manual says you can do that? I didn't think there was enough current available on a serial port to drive anything other than maybe a low end PIC... My preference would be to find a more reliable 5V line and connect that up.
Serial ports are weird, iirc the specification is really loose and you're expected to see anything between 5V to 20V at the receiver end, and to improve signal quality a "0" is a positive voltage beyond 5V and a "1" is a negative voltage beyond -5V. If you're going to use these, i'd suggest putting a zener diode across them. Does your manual say what you're supposed to plug the positive voltage lead into?