That's because the old one is a wireless thermostat... Honeywell TH6320R1004 Wireless FocusPro Thermostat

Most likely, none of those wires are actually hooked up to the air handler. It's possible the EIM is and that's where you'd want to install the new thermostat. https://www.amazon.com/Honeywell-THM5320R1000-Equipment-Interface-Module/dp/B004MH00VQ/ Link so you can see what to look for.

You're probably better off sticking with what you had or hiring a professional.