setTimeout and “this” in JavaScript

A more elegant option is to append .bind(this) to the end of your function. E.g.:

    setTimeout(function() {
        this.foo();
    }.bind(this), 1000);
//   ^^^^^^^^^^^ <- fix context

So the answer to the OP’s question could be:

    test.prototype.method = function()
    {
        //method2 returns image based on the id passed
        this.method2('useSomeElement').src = "http://www.some.url";
        timeDelay = window.setTimeout(this.method.bind(this), 5000);
        //                                       ^^^^^^^^^^^ <- fix context
    };