If you're asking about using the cable that came with the GPS to connect the PC to the hand controller, be careful! There is no standard for wiring of serial cables, and if you get it wrong, you could fry the hand controller, the mount, the PC or all three! The pin-out of the cable has to be correct, so you would have to verify that with a conductivity meter. And the PC cable port on the handset is RJ-12, not RJ-45, so an RJ-45 cable won't work.
You should already have a cable that works, though - the cable that came with the mount for downloading firmware is the same one you use for PC control through the handset. The cable that came with my Atlas is a little short, though, so I determined the pin-out and fabricated a longer one. Attached is a drawing I made of the Atlas serial control pin-out, it will be be same for the HEQ5.
If you're asking about the Serial-USB converter, some of them work to control the mount and some don't. My laptop PC has an RS-232 port, so I haven't used the converters, but you can give it a try. Use the cable that came with the mount until you get or make another one.
The Synta mounts with the SynScan controller will work with Cartes du Ciel and ASCOM with or without EQMOD software, and if you use EQMOD, you can use the mount with the handset or you can get an EQDIR module and use it without the handset. If you don't use EQMOD, you must attach the serial cable to the handset, and configure the mount as one of the Celestron Advanced Series EQ mounts in the ASCOM dialog within Cartes du Ciel. With EQMOD, you can connect the serial cable to the handset or to an EQDIR module.
I have used my Atlas mount in all three configurations with Cartes du Ciel. Going through the handset with EQMOD requires recent firmware in the handset so that you can enable PC DIRECT mode in the handset. It works fine, but there are problems if you try to take the handset out of PC DIRECT mode and use the handset for anything other than directional and slew rate control while connected through EQMOD.
My recommendation though is to get an EQDIR module and use it with EQMOD instead of the handset. You can buy an EQDIR module at http://www.shoestringastronomy.com, and they sell long cables too. You will then need a joystick or gamepad to control the mount in lieu of the handset. I use a Logitech Cordless RumblePad. EQMOD gives you much better control of the mount than the ASCOM Celestron interface, and the EQDIR supposedly gives you better tracking/guiding performance than going through the handset with EQMOD, though I couldn't really tell the difference.
please log in to view hosted photos in full size.