Do I have a shot at good business schools?

I'm 5 years out of college, I taught English internationally for 3 years after college, then went to work as a research assistant at a target school's graduate program. I am now about to enter as an analyst at an American bulge bracket bank's overseas office where they operate as a joint venture with a local company. I will be working in the office that oversees the joint venture. It is not client facing, but I will be reporting directly to the #3 person in the company, preparing the CEO's presentations, reports for the CEO and the executive committee and going to meetings of the board. I suppose this could be considered back office and that's why I'm a little worried about how it may look for business school. I will be getting paid what IBD analysts make and our entire office is me, an associate and 2 MDs, so fairly senior level. What are your guys thoughts?

Pros: I became close with my professor who is a Harvard PhD and one of his dissertation advisors was a HBS professor, while he is quite senior now, I imagine he still has contacts so he can put in a word

Can spin this as a reporting to the CEO type of position

Cons: It's not directly revenue generating

I will be old when it comes time to apply, about 29 or 30 years old...