I've not got a X5470, my 3-in-1 is a X2350 but when I put a compatible cartridge in I was able to print the alignment page but always had warnings of low ink. I think it's Lexmarks way of telling us to stop messing about. I'll do that when they radically reduce the cost of their own cartridges.
One bit of advice is to make sure that after you've filled the cart. make sure the print head is clean.