Hi Sam, and welcome to the forum.
As ChiefFourString said, slow down. The best way to build up speed is to start at a comfortable tempo, and build up the speed gradually.
Be careful with over stretching, especially on the lower (1-5) frets. If you over do it, you may have physical problems at a later stage. Use the thumb as a pivot to move the hand/fingers to where they are needed.
You have only being playing a very short time, so take it step by step, and be patient with yourself.
Give your hands and fingers time to adjust to this new task being asked of them. Speed will happen with time and practice.
Best of luck, and welcome to the low end !!
You may find this link useful. About half way through, he shows how to use the thumb as a pivot.
It is worth watching the whole clip though. http://www.youtube.com/watch?v=IeRoQuXlj9w