To directly answer your question...
There is no federal waiting period* for handguns let alone long guns. (For all intensive purposes we're referring to non-NFA firearms)
The waiting periods you hear about across the country are STATE mandated waiting periods.
The WA CPL allows your to cash and carry your firearm (meaning purchase it and walk out with it like you had just purchased some snow tires for your car). The CPL is a state issued permit and the 5day waiting period is a state law. The hiccup is the CPL in our state does not circumvent the federal mandated NICS check we are all so familiar with when we purchase a firearm.
So it looks like this:
Gear up to purchase your firearm.
State Mandated 5 day waiting period for handguns (CPL's exempt) proceed to step 2
Federal NICS check to ensure you have nothing preventing you from legally obtaining the firearm. Check comes back while you're in the store? Proceed to step 3. If not, proceed to step 4.
If you have a CPL and the NICS comes back clean. Step 5.
*If the NICS is delayed you have to wait until the feds call your FFL back to give you the green light before you take it home. If NICS never calls back the FFL must turn over the firearm to you. Step 5.
Get to the range!