Hi,
Hmm.... Dsl, always a tricky subject.
What sort of DSL - ADSL? Is it over standard analoque phone lines? (or cable?) The mention of copper is not so much for your internal wiring, but what is inbetween you and the exchange. If there is fibre or other connection types/links this can cause complications.
The first thing I would try is disconnect any phones (especially extensions) you may have, and plug the modem/router directly into the main socket (with no filter - that's only needed for phones). See what speeds you get then, and of the signal quality stats being reported change at all.
Here in the UK the adsl lines "learn" the best possible speed over about a week or so. It's recommended that you don't leave the connection on constantly during this. Switch the router off for 30 mins + at least once a day, and it should gradually adjust the line/rate to optimal settings (basically it works out the lines max stable rate).
If you have a standard wired phone, try plugging that into the master socket with a filter - is there any noise on the line? This can also only appear when the broadband is active - so also try a wired phone in the master socket with a filter when you have the router connected.
Is the rate you posted what you are getting on speed tests, or the actual connection speed being reported by the router?
Attainable rate: 5216/1088 Kbps
This seems to think you should be able to get 5,216 Kbps (BITS per second.

). There are two possibilities here - there is a problem with your line somewhere (you can at least determine whether its an internal or main line issue) or the best stable rate setting at the exchange has been set inaccurately low.
I had an issue where my broadband was only connected at 2048 Kbps, yet the signal quality ratings from my router was indicating it was possible for a lot higher. Every time I queried it with my provider (and them with BT) they checked on a database and said that according to that, that's the best I would get here.
I managed to get in touch with somebody via an adsl forum who maintained said database, who confirmed on my readings that it's capable of higher and amended it.
Next time I queried it with my provider it was changed straight away and I'm now connecting at 7,200 Kbps.
.....and then there was the whole issue with a spate of bad synch speeds and disconnections, which turned out to be corrosion in the BT line junction box on the outside wall of my house, but that's another long story.
Anyhow, try checking from your master socket first and if there's any noticeable problems you should get your line supplier to do a check on the line. If they find a fault they can sort it out for you.
Hope that helps?