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@inappropriate_bike
5k is a bloody long way in S London.
Sydenham/Kirkdale/Wells Park Rd/Taylor's lane/Longton Ave gets you to about 2.5k with a ramp at the end. It would need one marshal on the right turn but I wouldn't really expect any conflicting traffic.
You wouldn't need many laps of Westwood park / Canonbie up then down / back to Westwood park before people agree that they've done 5k and ask if they can stop.
If it's a Sunday, I think your best bet might be the quiet roads in the Docklands. Then cross the tunnel to do the hill climb at Greenwich.