I'm getting around 80% of my tuition paid in athletics scholarships, so that's something. I did a few road races and got some $, but nothing crazy (500$ max I think). Once I graduate I doubt I will get any real money (in the sense that I won't have to work a real job) from running unless I can get down to something really fast like ~13:15.
I would definitely not count on a high 13 min 5k to consider running as a career ... unfortunately keep studying! Read the zane Robertson thread / interview if you want to understand how difficult it is to make running your career.
Btw - I was running high 16 mins in the 5k at 18 and broke 14 mins at 21 - so don't believe all the people here saying that it's impossible.