First thing first, you need a small file named NikonUsbScanners64.zip, which contains information that will lead Windows to recognize your device as a scanner. Get it there and save it to some place on your hard disk, for example in your Documents folder (the actual location is unimportant, just make sure to know where you put it as you'll need to refer to that location later). Unzip the file: you should end up with a readme.txt file, NikonUsbScanners64.cat and NikonUsbScanners64.inf - note that there is no .sys and nothing executable, and that the relevant files are digitally signed.
Next, download the last version of Nikon Scan (4.03 at the time of this writing) from the Nikon website, then proceed as follow:
Plug the scanner in a free USB port, turn it on and let Windows try, and fail, to find a driver for it, then...
1) Open the Device Manager (the quickest way is to click the Start button on Windows' taskbar, type Device Manager in the search box, the start menu should soon display the needed entry, click to open). Windows 8.x users can simply type Device Manager on the start screen, then look under Settings.
2) In the Device Manager window, locate the LS-5000 ED scanner (or LS-40 / LS-50) under Other Devices, then right-click the scanner's name and click Update Driver Software...
3) Click Browse my computer for driver software
4) Type the name of the folder where you have unzipped the driver files (or use the Browse... button to navigate to that folder) and click the Next button.
5) Click Install on the Windows Security prompt, then click Close after Windows finished installing the driver.
Finally, install Nikon Scan 4.03 normally, but be sure to uncheck both drivers (LS-4000 / 8000 / 9000 and LS-40 / 50 / 5000) on the Select Drivers page.
That's it. The 32-bit Nikon Scan 4 should work fine on Windows 7 64-bit (and Vista) and your scanner should be found and recognized. You can now delete the zip, readme, cat and inf files, they are not needed anymore.
EDIT: Aug 24, 2013 - The driver information file is now signed with Axel's VeriSign Class 3 digital certificate, which should remove the warning that was displayed on Windows 8.x
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