Based on the numbers you gave, his weight is appropriate for his height, however his height is well below the 5th percentile for his age. As you suggest in your question, one would expect him to be taller given your height and his father's height, however there are a number of other things that could affect this.
There are some children who are short because their maturation is delayed. These children typically start puberty a bit later than usual and continue growing when they are 17 and 18. They ultimately end up at the "right height" but it just takes longer to get there. There are also a number of endocrine or nutritional problems that could affect a child's growth, and not all causes of "underheight" are suitable for Human Growth Hormone treatment.
I recommend that you make an appointment with your pediatrician to specifically address this question. Your pediatrician can review his previous growth pattern, review his medical history, and do a complete physical exam to look for signs of other problems. He may need to get some simple blood tests, or an x-ray to look at bone maturation. Based on this, your pediatrician can decide if your son might need further evaluation or referral to an endocrinologist.