Medicine at Cambridge University. Should I still bother?

Hey, I got 5A*s and 6As at GCSE and I want to do medicine. Should I still apply to Cambridge University? Please be realistic and don't sugarcoat! The statistics for 'oxford medicine' says 10A*s is the average for an offer holder, so I'm assuming it would be similar. Is there anyone doing medicine in Cambridge with similar grades to what I have achieved?

(Hypothetically speaking assume I will achieve 2A*s and an A at A-levels at a decent sixth form, have plenty of work experience/volunteering, have chosen the 'right' subject combination and have a good BMAT score)

Note: I'm also from a comprehensive school (but not below average) and have a chronic illness, but it was in remission during the exam period so I assume I can't go through the Extenuating Circumstances route.

It's really impossible to say how much your possibility of getting offer for Medicine just with GCSE results. Hypothetical question only leads to hypothetical answer, you know?
What's important thing for you is to choose right A-level subjects and work very hard to get necessary grades and do all the right things like work experience/volunteering, reading subject elated books, etc. etc.
Just FYI, most of successful candidates for Medicine achieve 3 or more A*s.

For applying to Cambridge, there're lots of useful info in this post.
http://www.thestudentroom.co.uk/showthread.php?t=3554013&p=58964173#post58964173