You can give this a try
Make your way to Control Panel > Devices and Printers > Add a printer.
It will prompt you for a printer connection. Select the USB option.
Use the Windows Update button to expand the list of supported printers. It takes a few minutes to do.
Now look in the HP list for the Deskjet 5600 series. There are two and I am not sure which one will work, so you may have to try both.