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I see from the post that you are having issues printing in black on your HP Envy 5640 printer. Don't worry as I have a few steps to help you get through this concern,
To provide you with an accurate solution, I'll need a few more details:
Have you recently made any changes on the printer before the issue started?
Are you able to make a copy from the printer?
Have you tried to clean the cartridge contacts as well as the rollers?
In the meantime, let's start off by performing a Hard reset on the printer and make sure that the printer is connected directly to the wall outlet and not to the surge protector.
Remove all the ink cartridges and then try to perform a hard reset on the printer.
With the printer turned on, disconnect the power cord from the rear of the printer and also unplug the power cord from the wall outlet.
Remove USB cable, if present.
Wait for 2-3 minutes, press and hold the power button on your printer for about 30 seconds to remove any additional charge.
Now plug back the power cable straight to a wall outlet without any surge protector or an extension cord and then plug back the power cord to the printer.
Turn on the printer and wait till warm-up period finishes and the printer is idle.
Now insert the ink cartridges and then try to print a test page and check if it works.