As an occupational therapist, I'd like to respond to those who wonder why the "correct" pencil grasp is important.
First, why do kids use funny grasps? The grasp they use is primarily an indicator of the maturity of the hand in its development. Many children are introduced to using pencils and crayons before the hand is mature enough, and form permanent habits of a poor grasp. I think it very important not to introduce kids to printing letters until the hand is mature (age 6-7 in America). Doing other fine motor tasks that develop the ability to use a variety of grasp patterns with the fingers, and fine manipulative skills is the key to developing the hand.
Why is the correct grasp important? The problem with maladaptive grasps is that while they serve to give the child a sense of control over the pencil at a young age, these patterns become habit from practice (practice makes permanent! to quote a famous OT, Mary Benbow), and ultimately slow them down later. The hand is a precision built machine, and its most efficient patterns of movement are the ones we consider "normal" - in these movement patterns, all the joints and tendons and muscles are alligned, so that the hand will work efficiently. Without this the hand fatigues, gets cramps, and the child does not develop speed in their writing, required for later school tasks. In addition, poor grasp patterns may lead to damage to joints and ligaments, contributing to deformity ultimately.
Better to wait for maturity of the hand before introducing pencils, than to try to rush development of skills beyond that readiness.
The suggestion about small pencils is a good one for 5 year olds - I like using crayon stubs even. The other key is to have the paper well onto the table, rather than lined up on the edge. This way the child can rest the arm on the table, and just use the hand and fingers to control the pencil.