I'm five weeks pregnant and my heart rate has gone from a normal of about 68 to around 105 resting. is this normal?

Possibly: This can be a normal event but it would be good to know if you had any history of heart or blood pressure problems. Please see your family physician and/or your OB-GYN.

Don't worry, but: Since this is a bit high - do ask your OBGYN about it and keep track. If there's no other problem it may be a normal fluctuation - call them to ask and perhaps move up your next appointment. Don't worry, just call. Hope it's nothing or that it can be easily addressed. Best wishes!