According to the AirPrint page list here, About AirPrint - Apple Support the HP 5470 series is not listed as AirPrint compatible. However, if you go to the HP website, it appears the device supports AirPrint. It doesn't have to do with your ISP, it has to do with your wi-fi network. Both devices have to be connected to the same wi-fi network for it to work on the iPad. I'm not sure what it takes for the Mac, as I am not a Mac user. If you cannot get it to connect for the iPad, or want further instructions about AirPrint capability, see the support document.