I have my HP 5490C (which is the designation given to an HP5470C once
the ADF is installed) working successfully on Windows 7 32-bit.

To get it installed, I applied the following combination of parameters:

-Windows XP SP2 compatibility mode
-"Run as Administrator"
-Give "Everyone" "Full Control" permissions

To BOTH the installation (setup) program and the applications (HP
PrecisionScan Pro and the other .exe file utilities) that it installed .

IT DOES WORK.

The one note I'd make is that I get a UAC prompt every time I start the
scanner (e.g. every time I start HP PrecisionScan Pro). For now, I have
disabled UAC, but I may turn it back on and just accept the
inconvenience. Also, while installing some windows update updates AFTER
I had installed this, one of the optional updates for Win 7 was an
"compatibility enhancement" that makes Win 7 more tolerant of older
programs. This, too, might address the UAC issue. But the UAC issues
is an annoyance, not a show stopper. The real news is that the 5470C /
5490C scanners CAN still be used under Windows 7, or, at least it seems
that way. Two things I have not yet tested are ADF scanning and the
twain and WIA interfaces to other programs (in particular Adobe Acrobat
and CardScan). I will be testing those in the next week or so as I add
software to my Windows 7 installation.