Hi,
The HP Photosmart C4580 All-in-One Printer support page shows drivers for older Mac operating systems only.
However, you may want to check whether the HP 5.1.1 Printer Software Update at https://support.apple.com/kb/DL1888?viewlocale=en_US&locale=en_US contains something useful. An HP Photosmart C4500 series version 5.0.5 printer driver is mentioned in the article Printer and scanner drivers for Mac - Apple Support.
If necessary, you could also try resetting the printing system and (re-)adding the printer.
Reset the Mac printing system to solve a problem – Apple Support (UK)
Add a printer on Mac – Apple Support (UK)
Make sure that you have backup copies of all important files (documents, photos, et cetera) before testing anything.