installed a new ink cartridge and printer won't accept it

[Bob19752]

new ink cartridge not accepted by printer.  Message says ink cartridge must be replaced

[Rainbow23]

Hi @Bob19752,

Welcome to HP Support Community. 
Thank you for posting your query. I will be glad to help you.

I see that you are facing cartridge issues with your HP ENVY 5530 E-All-In-One Printer.

Please follow the steps listed below to clean the electrical contacts of the cartridges:
1. Turn the printer on.
2. Open the door to access the cartridges.
3. Wait until the carriage stops moving before you continue.
4. Remove the cartridge indicated in the error message from its slot, holding it by its side.
CAUTION: Do not touch the copper-colored contacts or the ink nozzles. Touching these parts can result in clogs, ink failure, and bad electrical connections.
5. Remove any protective tape that still might be on the contacts.
CAUTION: Do not touch or try to remove the copper electrical strip.
6. Lightly dampen a lint-free cloth with distilled water, and then clean only the copper-colored contacts on the cartridge.
7. Lightly dampen a lint-free cloth with distilled water and then clean the electrical contacts in the carriage, located inside the printer.
8. Wait 10 minutes for the contacts to dry.
9. Reinsert the cartridge.
10. Close the cartridge access door.
You may also refer to the steps in this document 

Let me know if this helps.
Take care and have a great day ahead.

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