Something is "off" here... your LMP says May 16th, your ultrasound says May 26th, but you're measuring 5 weeks ahead? According to what? Your ultrasound would have you 10 days "small" for your LMP date... are you referring to the measurement they take at your appointment? Those are wildly inaccurate.
It's all a guessing game. There's really no way to know exactly what day your baby was concieved AND implanted. Due dates are based on averages. The average pregnancy is 38-42 weeks, hence the "40 week" date you are given. In all reality, most babies are born within 3 or 4 days of that date in either direction. HUGE margin of error there!
As my doctor has said... he wishes they gave out "ballpark dates" rather than specifics, but the insurance companies want something more exact. I'm due on April 16th according to my LMP and 18th according to my last ultrasound. My doctor has told us not to plan anything after the 13th to be safe.
Good luck. Ask your doctor at your next appointment where they are getting the measurement from. If it's your fundal height, it could be more of a reflection of the weight gain than the development of your child- which is really only observed through the ultrasound.
Could you go into labor early? Sure. More likely, if you have a really big baby, they'll schedule you for an early induction or c-section.