in my opinion, your age is by no mean a problem. You have an interesting balanced profile (charity is always great to have on a resume), with PE experience which tend to be appreciated by admission staff. You have a clear career plan, which is useful for your essays.
However, the relatively (I insist on the word "relatively, which means they are not "absolute") "weaknesses of your profile might be the fact that your undergrad and grad institutions are not presitgious, and that your GMAT is good, but not outstanding for a top 5 program.
So the advice would be to work very (very very) hard on your essays: it can change everything (I have a friend who went to a top 10 B-school with 650 on the gmat, 2 years of experience in an obscur and little private French company, and a GPA close to 3.2). Try to make the most of your recommendation, even if I am not convinced by the impact on the application.
However, the competition for the top 5 is very tough, so you have to be aware of that before applying. You have some chances to get in, but that is by no mean certainty.
I hope this was helpful, I wish you all the best for your applications.