Hi and welcome to the forums
There is no official Windows Vista/7 drivers for this device however that may not be the end of the story.
Try using the driver in compatibility mode with Windows XP.
This can be done by downloading the driver & installer program from HP Scanjet 5370c Scanner series- Download drivers and software - specify product name - HP Business Support Center
and right clicking on the installer program. Go to the Compatibility tab and set the compatibility for Windows XP SP2.
There is a high likelihood that this wont work in which case the only advice I can give you is to buy a new scanner.
Please post back with any results and any queries you may have.
PS This forum is reserved for questions about Windows Vista only. If you have questions about Windows 7 please use our sister site Windows 7 Forums