Hello susanleehelp,
Welcome to the HP Support Forums!
I see you are having black printing issues on the Officejet 5610 after changing the ink. I would like you to print a self test, this HP document: Faded or Dull Colors in Printouts will teach you how and show you what it should look like. Only follow the troubleshooting in that document if the self test does not print correctly.
I would like you to run the HP Print and Scan Dr on the computer to check for driver / software issues. If there is a driver / software issue this should clear it up.
Thanks for posting and I will keep an eye out for your reply,