USB extension

Maybe. The problem is the DC resistance of your CAT5 extension cable. If you inspect the official USB cable, the outer two wires are typically #20 awg. Your single pair of CAT5 is #24 awg or about twice the DC resistance per ft. Even so, the maximum length for USB, without repeaters, is about 16ft.

I think you can make this CAT5 kludge work if you use one pair for data, and parallel the remaining 3 pairs to supply the DC power.

Once you have 5.0VDC delivered to the DWL-122, then start thinking about shielding. You may not need it.

OTOH, I thought the 16-foot limit on USB was due to timing, and I've had several nightmares trying to make HP AllInOne devices work on "active extensions" (16-foot cables with bus-powered 1-port hubs molded into the ends), so I'd proceed with caution.

Maybe placement of your USB WiFi adapter on a legal-length 16-foot cable (up instead of over, etc) would work better...

I might think so. A 5 meter USB cable is about $10 or less around here. That works quite well with my DWL-122. Shielding or power loss (I know the DWL gets warm, so it's drawing more power than you might think), or just bad connections.

Where is the router? Since you have a 20 ft cable, wouldn't it be eaiser just connect the PC to the router with cat 5 cable directly?

Again, try going up 10 feet instead of over 20 feet...