How to deal with disagreement with advisor regarding research proposal and direction?
I have regularly had problems with my supervisor regarding scientific direction. I have always known that I write much better than I speak. About 6 months into my PhD I reached the conclusion that its possible that I am not able to coherently convince my supervisor regarding my ideas and reasoning. 

This has in fact been pointed out to me by my PhD advisors and also the examination board. In their words, I have an extremely unstructured, abstract and convoluted line of thought. Although, I may reach at the same conclusion, my process is not easy to understand for other people.

So what did I do? 

I adopted the show them before telling them process. So whenever I wanted to introduce new ideas to my supervisor, I would generate data for the same, create a presentation and then speak to them. This mostly meant that my supervisor got the point.

In you case, that may not be possible because your application is due in 5 days.

In that case, I would suggest you write up an alternative draft containing your vision of the proposal. Do this, but also complete the proposal your advisor wants you to write. Before submission, when reviewing the drafts send both proposals to him in a politely worded e-mail asking him to review both.