In your circumstances, all you need are 2 days in a row of moisture-free weather. The logic is you don't want to seal any moisture in the wood by staining it too soon. If you know you can get away with more time for it to dry out, the better. You must, however, read the can of stain and see what it says as far as drying time.
So, if the weatherman can assure 5 good days of dry weather, then you can have the deck dry out for 3 days and, if the can says you need 2 days for the stain to dry, then that's a total of 5 days. Best to ya and hope this helps.
PS: The 'washing' of the deck is for removing dirt and mildew and any UV-damaged wood in preparation for a sealer, a stain, or paint.