Thanks for the info, Llewen... I am pulling my hair out on this one... and now so is my ISP Tech guy!
The router is connected directly to my computer via Ethernet. I've done everything you've said, and it doesn't point directly at my Actiontec Wireless DSL router/modem. But one very strange thing is, if I reboot or rest my modem, the start time of the 5-minute interval to disconnect changes. I called Actiontec and they said that doesn't mean anything... but seems strange to me. They said they would replace the modem, but it's 65 miles one-way to the nearest store that carries a DSL modem, on a guess that is the problem.
The router/modem has the latest firmware. I've rebooted, reset, and reconfigured the router settings several times, and no change. I'm 90% sure it isn't the router. But not 100%.
I spent an hour or so this morning on the phone with my ISP Tech, watching pings along the route. At exactly 5 minute intervals, exactly one packet is dropped and I get disconnected. Exactly one packet each time. We were polling each hop, thousands of times, but it is so hard to find where that one packet was dropped from. I ran 6 simultaneous and separate trace routes, polling each hop separately for over an hour. I can time when the packet will be dropped, we just can't see where it originated from.
Sometimes... I just hate technology.