My 5 year old son has a very weak urine stream, is this a problem?

Usually is. How much of a problem it is depends on the findings. By age 5 circumcised males may develop a narrowing of the urine outlet of the penis. It is less common for uncircumcised. If they have a mild inflammation at that site, conservative treatment with meds may improve it. Often it provides enough of a problem that the kid needs to have the outlet widened (dilated) by a urologist (under anesthesia.
Possibly, yes. Yes, this could be a serious problem. Take him to the pediatrician.
Weak urine stream. A weak urinary stream need to be evaluated by a pediatric urologist, a voiding cystourethrogram need to be done to check for narrowing or any form of obstruction. So please see your pediatrician & request a referral to a pediatric urologist. Good luck.