You can probably get by with a $3000 house payment per month on a $5500 take-home pay, as long as you are willing and able to sacrifice some aspect of your life (i.e. vacation, having a nicer car, buying nicer furniture, etc.). I personally would not do that simply because I enjoy taking vacations and spending money on a lot things that I probably don't need.

Normally industry experts recommend that the housing cost to be less than ~40% of your gross pay. Your gross monthly pay is probably around $8,500, which will make your housing payment ~35% of your gross pay. Pretty high percentage, but still be okay as long as your financial condition does not change significantly.