It could be done quicker if PDgives an "OK" sooner than 5 days. I believe most PD's don't notify of the OK's, in which case it defaults to5 business days. Many dealers are now saying "up to" 10 days due to weekends and holidays.
If you are new to WA., don't have WA DOL/ID or haven't been a resident for 90 conecutive days, the wait can be up to 60 days.
From RCW 9.41.090...
(1) In addition to the other requirements of this chapter, no dealer may deliver a pistol to the purchaser thereof until:
(a) The purchaser produces a valid concealed pistol license and the dealer has recorded the purchaser's name, license number, and issuing agency, such record to be made in triplicate and processed as provided in subsection (5) of this section. For purposes of this subsection (1)(a), a "valid concealed pistol license" does not include a temporary emergency license, and does not include any license issued before July 1, 1996, unless the issuing agency conducted a records search for disqualifying crimes under RCW 9.41.070 at the time of issuance;
(b) The dealer is notified in writing by the chief of police or the sheriff of the jurisdiction in which the purchaser resides that the purchaser is eligible to possess a pistol under RCW 9.41.040 and that the application to purchase is approved by the chief of police or sheriff; or
(c) Five business days, meaning days on which state offices are open, have elapsed from the time of receipt of the application for the purchase thereof as provided herein by the chief of police or sheriff designated in subsection (5) of this section, and, when delivered, the pistol shall be securely wrapped and shall be unloaded. However, if the purchaser does not have a valid permanent Washington driver's license or state identification card or has not been a resident of the state for the previous consecutive ninety days, the waiting period under this subsection (1)(c) shall be up to sixty days.