The answer's found in a section of state law called WAC 284-30-500(3). (WAC stands for Washington Administrative Code.) Here's the key section, with some highlighting we added:
(3) It is an unfair practice for any insurer to consider traffic violations or accidents which occurred more than three years in the past, with respect to the acceptance, rejection, cancellation or nonrenewal of any insured under a private passenger automobile insurance policy, unless, because of the individual's violations, accidents or driving record during the three years immediately past, the earlier violations or accidents are significantly relevant to the individual's qualifications for insurance.
So insurers generally cannot use the older data as a basis to reject/cancel/non-renew you, but there is no prohibition against using the older data to assess risk and rate -- meaning set the cost of -- your auto policy.
Even if you have a problem driving record, it's always a good idea to shop around for alternative rates, since insurers don't all charge the same rate for the same level of coverage.