Hi Ann, Not sure what to suggest as I don't know this printer with 5 colour cartridges but looking at HP web site, it uses the normal Cyan, Magenta and Yellow, the extra two being a lighter blue and a lighter red.
You could try printing Test page No. 5# from the pages previously suggested by Scotsman on your normal Kodak paper and then turn the paper over and print the same test page on the reverse (plain side) of the Kodak paper.
If the colours are different then the special photographic surface could be having some effect on the ink supply.
If both printed sides are both the same then maybe the thickness of the Kodak paper is causing a different printout than the A4 paper, which doesn't really make any sense, does it?
See how you go with the printed Test page above unless anyone else who has this printer can offer a better suggestion.
Incidentally, do you tell the printer (in the set-up) that you are using a different paper, A4 or Kodak?? If you do, try using Kodak paper but tell it that you are using ordinary A4.