Generally speaking you want to try to at least hit a school's average or they will place additional weight on the other parts of your app - looking for proof that you are up for the rigors of their school. In your case, the Fulbright & work at Google will definitely help, especially if you've made significant impact in your role at Google. You also might want to consider taking a quant class (assuming your quant score is low) to show that you are making an effort to address that weakness.
Even with a Fulbright and work at Google, low 600s is pretty low & is going to make top 5 tough. I'd shoot for at least high 600s.
If you think you might have a learning disability it also might be worth getting tested/seeing a specialist. If you could get documentation of that you could get extra time on the GMAT & could also mention it in an optional essay when you submit your app. If you can show that you can still get a solid score (with that extra time) & have kicked butt at work even with that learning disability you could even turn that into a strength of your app (i.e. ability to overcome difficult circumstances).