The US Customs and Border Protection site gives information on your son's type of situation. They answer the question "Will I be arrested when I re-enter the U.S. if I have unpaid traffic tickets?"
Customs and Border Protection (CBP) consumer center answer is that they strongly advise you to pay your traffic tickets, particularly moving violations. While unpaid tickets would not subject you to arrest unless a warrant is issued, you may be subject to a more intensive inspection if your record is not clear.
So it does not appear that your son would be denied entry or arrested at the border however he may be put under more scrutiny by the CBP. If your son drives in Washington State and is stopped by law enforcement then it is likely he would be arrested. Normally if you do not pay your traffic tickets then you are convicted in court for failure to pay or failure to appear on the citation and an arrest warrant is issued.
[Let CarInsurance.com help you find affordable auto insurance now.] We are not aware of any statute of limitations for traffic tickets for any state. If that was the case people would just wait out the period and not take care of their tickets or court dates. Instead what happens is if you fail to pay the ticket or appear in court to take care of the ticket there then you are usually found guilty by the court and given the penalties for the violation. If you then fail to pay the fine or otherwise take care of the penalties assessed for the traffic ticket by the court your driver's license or driving privileges are suspended by that state until the ticket is taken care of.
Normally states will send tickets that go unpaid to collection agencies that will find you and hound you for the fine amount, plus now also late fees and collection fees. So it is important to take care of traffic tickets outside of your area of licensing if you plan to ever go back to that area again.
One Washington District Court states that you must respond within fifteen (15) days of the date that a traffic ticket was issued. An infraction is not a crime, but failure to respond can result in the suspension of your driver's license.
A failure to pay or respond to the ticket within 15 days results in an order that the infraction was committed. If you asked for a hearing and do not appear your payment is due immediately. When an infraction is not paid in a timely manner or a hearing missed, a $52 late penalty is added to the amount shown on the ticket. Your license may then be suspended if the penalty is not paid following a notice to pay the increased penalty, and the account may be assigned to a collection agency.
While your son may not be held at the border or arrested for just entering Washington State, if he is stopped by police and they find that he is driving on a suspended license, due to the failure to pay the ticket from 5 years ago, then he could be written up for driving on a suspended license.
RCW 46.20.345 which states that any resident or nonresident whose driver's license or right or privilege to operate a motor vehicle in this state has been suspended or revoked as provided in this title shall not operate a motor vehicle in this state under a license, permit, or registration certificate issued by any other jurisdiction or otherwise during such suspension or after such revocation until a new license is obtained when and as permitted under this chapter.
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A person who violates the provisions of this section of WA law is guilty of a gross misdemeanor. In Washington state gross misdemeanors are punishable by up to one year in jail and/or up to a $5,000 fine.
If your son knows the county where he received his ticket he may want to contact that courthouse to see how to take care of this old ticket. If he does not remember then he may see if the WA Department of Licensing (DOL) could help him clear up this old traffic infraction so that if he goes to Washington State he will not have any issues. | 
