R., children mature at their own rates. The number 5 1/2 is a ball park figure. so I wouldn't worry if I were you. But if you do think he might have a medical problem do take him to the doctor.
I am really confused. You suggest that he may have a medical problem when you ask if you should take him to the dr. but yet you've tried punishment to get him to stop.
Until a child's bladder and sphincter muscles are fully developed wetting their clothing or their beds is not completely under their control. The ability to stay dry at night develops later than the ability to stay dry in the daytime.
Two of my brothers wet the bed until after they started school. Our family had alot of stress and I suspect that is why it took them so long to be able to be dry at night. My parents also limited their fluid intake and it helped some in that there wasn't so much urine but they still wet their bed. And they got them up during the night. This helped some of the time. They put rubber sheets on their bed. And never did they chastize them for doing something over which they did not have control. They sympathized with their embarrassment and reassured them that they would eventually be able to stay dry.
My parents were concerned that there could be a medical problem and took them to the dr. They did not have a medical problem but were tense and anxious about the stress going on in our home. They wanted to stay dry. They cried sometimes when they woke up wet.
At 5 1/2 your son's physical ability to stay dry at night might very well not be mature enough. He could also be tense, anxious, about wanting to please you but since he can't stay dry he can't please you. This puts a lot of pressure on him which will add to his inability to stay dry even if he were physically able to stay dry.
50 years ago they didn't have some of the conveniences we have today. No pull ups. No disposable bed pads.
I recommend that you put him into night time pull ups and tell him that some kids just mature later than others and he'll stay dry when he's able to stay dry. Not to worry! Today's night time pull ups look much like regular underware. They will help him feel more normal.
If money is a problem, look in thrift stores for the bed pads used in hospitals and nursing home. I've found several at less than $3/piece. You can also find sheets at a thrift store and boy's undershorts are about $6 for a pack of 4 at places like K-mart. Have enough so that you can still do laundry just once a week.
And be assured all children eventually stay dry. What is important is to not pressure them to do it on your time schedule. Accept that he is doing the best he can and reassure him of your love even if he wets the bed.