I have an hp envy 5660. what app do I need to AirPrint?

The HP Envy 5660 is Airprint compatible according to the compatibility list in the link below, so you don’t need any app.

About AirPrint - Apple Support

Simply select the Pint option in whichever app you want to print from, and it should appear as a selectable printer in the printer list.

As mentioned, both printer and iPhone need to be connected to the same Wi-Fi network.

Details here: Use AirPrint to print from your iPhone, iPad, or iPod touch - Apple Support

Here is a list of AirPrint compatible printers. Your printer is on the list, so you don’t need to install anything. It will just work when you choose “Print” in any app.

If your Envy is AirPrint compatible connect it and the iPhone to the same WiFi network.