Almost certainly not, no. I think service tends to run out at around 2km, possibly up to 2.5km
The VDSL2 used in the cabinets, in theory, drops to the same speed as ADSL2+ at longer distances. By that statement, most people focus on the downstream speeds.
However, the way things have been set up, it just doesn't happen in practice:
1) The very lowest frequencies, that overlap ADSL and ADSL2+ from the exchange, are deliberately crippled in the cabinet - the "PSD mask" reduces the transmit power of those frequencies (as transmitted by the cabinet) to ensure that they don't interfere with signals from the exchange.
As a consequence, you can't actually get a better speed from the cabinet than you can from the exchange, once you've gone far enough away from the cabinet to be left with those frequencies alone.
2) The limiting factor, at the longest distances, seems to be the upstream speed. You run out of connectivity here first, before you run out downstream.
I'm not sure why this is. Power shouldn't be an issue here.
Anyway, there have been a few reports of speeds in the 1.6km - 2km region where they got 18Mbps down and 1.2Mbps up - although those were probably "early adopter" speeds without much crosstalk present.