Very possible... but without knowing your actual credit scores, I cannot determine this.
Now, you have $10,000 down, but do you also have another 10k for closing costs? Closing costs vary from state to state... so sit down with a lender and discuss your down payment, and closing fees. There is a lot involved.
You could probably put less down as well with a 3.5% FHA loan. However also weigh in that FHA loans now require PMI insurance to the life of the loan... if you do conventional you can get rid of PMI if you put 20% down. You can put less than that down of course with conventional, but the more you put down, the closer you gain to being able to rid yourself of PMI