Twelve minutes ago, I got the wireless card working with my WPA-PSK home network.
A combination of the progress made on drivers over the last year, and finding which of the squillions of instruction sets out there Actually Worked has finally got things going – rather than recount it all here, I’ll point owners of the HP Pavilion dv5157eu to this page, and advise everyone else as to how I found it: do a Google search for some combination of ‘ubuntu’, ‘wireless’ and your laptop’s exact model number.
Edit: My wireless happiness sadly didn’t survive a hibernate or a reboot. Turns out the line of the page which says do ‘sudo echo ndiswrapper > /etc/module’ actually means, as far as I can tell, that you should do:
sudo -s echo ndiswrapper >> /etc/modules
As ever, follow my advice at your own risk.