I don't know how to create android apps. Here's what I want to accomplish:
User presses "My Game App" and launches, connects to chrome cast
1 Button on my Android device called "jump"
1 Button on my Iphone device called "jump"
I would like the "server logic" to be done with HTML 5 and javascript, my preferred language.
How does all this work together? Do I need to know 5 different device programming languages to do this?
The receiver app (what you call the 'server logic' will be written in HTML5, javascript, and CSS. However, the sender-side apps must be written in a language native to the platform that the users are interacting with ... so you'd need an Android app and an iOS app, and an HTML5 sender app if you want users to be able to connect from Desktop Chrome as well.
(And when I say 'native,' this generally implies Java for Android and Objective-C for iOS, but I have seen a few projects that are trying to get a Cordova plugin working to let you write a Cordova/Phone Gap-based app with Chromecast support.)