Would £5000 cover the cost of a boris bike station instead?
The system is owned by TfL (although obviously with engagement with councils) and a lot of the direct day-to-day management (maintenance and re-location of bikes for example) is outsourced to Serco.
Depending on location, installation requirements etc, it's about £200,000 to install a docking station.
There's also the need to consider the overall network. Fairly pointless installing a single docking station in (say) Dulwich Village - you'd want a couple in Dulwich Park (say one at Court Lane entrance, one at College Road entrance), one in the village, one up by Dulwich Library, three or four down the length of Lordship Lane, one each at ND and ED stations....
And then they'd need to link up with the next available docking points which are Brixton / Stockwell and up the Walworth Road, all of which are a reasonable distance away. So you'd probably need some "linking" docking points in Herne Hill, southern Camberwell / Denmark Hill and so on to tie it into the remaining network.